How to find an angle in an acute / obtuse triangle - ACT Math

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Question

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

Answer

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

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Question

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

Answer

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

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Question

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Answer

The measure of $\dpi{100} \small \angle ADB$ is $30^{\circ}$ . Since $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear, and the measure of $\dpi{100} \small \angle CBD$ is $60^{\circ}$ , we know that the measure of $\dpi{100} \small \angle ABD$ is $120^{\circ}$ .

Because the measures of the three angles in a triangle must add up to $180^{\circ}$ , and two of the angles in triangle $\dpi{100} \small ABD$ are $30^{\circ}$ and $120^{\circ}$ , the third angle, $\dpi{100} \small \angle ADB$ , is $30^{\circ}$ .

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Question

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

Answer

Interior angles of a triangle always add up to 180 degrees.

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Question

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Answer

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

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Question

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

Answer

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Compare your answer with the correct one above

Question

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

Answer

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Compare your answer with the correct one above

Question

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Answer

The measure of $\dpi{100} \small \angle ADB$ is $30^{\circ}$ . Since $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear, and the measure of $\dpi{100} \small \angle CBD$ is $60^{\circ}$ , we know that the measure of $\dpi{100} \small \angle ABD$ is $120^{\circ}$ .

Because the measures of the three angles in a triangle must add up to $180^{\circ}$ , and two of the angles in triangle $\dpi{100} \small ABD$ are $30^{\circ}$ and $120^{\circ}$ , the third angle, $\dpi{100} \small \angle ADB$ , is $30^{\circ}$ .

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Question

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

Answer

Interior angles of a triangle always add up to 180 degrees.

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Question

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Answer

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

Compare your answer with the correct one above

Question

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

Answer

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Compare your answer with the correct one above

Question

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

Answer

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Compare your answer with the correct one above

Question

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Answer

The measure of $\dpi{100} \small \angle ADB$ is $30^{\circ}$ . Since $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear, and the measure of $\dpi{100} \small \angle CBD$ is $60^{\circ}$ , we know that the measure of $\dpi{100} \small \angle ABD$ is $120^{\circ}$ .

Because the measures of the three angles in a triangle must add up to $180^{\circ}$ , and two of the angles in triangle $\dpi{100} \small ABD$ are $30^{\circ}$ and $120^{\circ}$ , the third angle, $\dpi{100} \small \angle ADB$ , is $30^{\circ}$ .

Compare your answer with the correct one above

Question

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

Answer

Interior angles of a triangle always add up to 180 degrees.

Compare your answer with the correct one above

Question

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Answer

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

Compare your answer with the correct one above

Question

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

Answer

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Compare your answer with the correct one above

Question

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

Answer

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Compare your answer with the correct one above

Question

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Answer

The measure of $\dpi{100} \small \angle ADB$ is $30^{\circ}$ . Since $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear, and the measure of $\dpi{100} \small \angle CBD$ is $60^{\circ}$ , we know that the measure of $\dpi{100} \small \angle ABD$ is $120^{\circ}$ .

Because the measures of the three angles in a triangle must add up to $180^{\circ}$ , and two of the angles in triangle $\dpi{100} \small ABD$ are $30^{\circ}$ and $120^{\circ}$ , the third angle, $\dpi{100} \small \angle ADB$ , is $30^{\circ}$ .

Compare your answer with the correct one above

Question

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

Answer

Interior angles of a triangle always add up to 180 degrees.

Compare your answer with the correct one above

Question

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Answer

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

Compare your answer with the correct one above

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How to find an angle in an acute / obtuse triangle - ACT Math

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B? A (Angle A = 41°) B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is: 41° + 41° = 82° Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180: 180° - 82° = 98°

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4. Find the measure of .

The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is . Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

Interior angles of a triangle always add up to 180 degrees.

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B? A (Angle A = 41°) B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is: 41° + 41° = 82° Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180: 180° - 82° = 98°

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4. Find the measure of .

The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is . Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

Interior angles of a triangle always add up to 180 degrees.

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B? A (Angle A = 41°) B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is: 41° + 41° = 82° Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180: 180° - 82° = 98°

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4. Find the measure of .

The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is . Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

Interior angles of a triangle always add up to 180 degrees.

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B? A (Angle A = 41°) B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is: 41° + 41° = 82° Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180: 180° - 82° = 98°

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4. Find the measure of .

The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is . Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

Interior angles of a triangle always add up to 180 degrees.

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.