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High School Math : Triangles

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Example Question #1 : Acute / Obtuse Triangles

In the picture above, $\overline{AB}$ is a straight line segment. Find the value of .

Possible Answers:

Correct answer:

Explanation:

A straight line segment has 180 degrees. Therefore, the angle that is not labelled must have:

$180-110 = 70^{\circ}$

We know that the sum of the angles in a triangle is 180 degrees. As a result, we can set up the following algebraic equation:

70 + x + x = 180

Subtract 70 from both sides:

2x = 110

Divide by 2:

x = 55

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Example Question #51 : Triangles

Rt_triangle_letters If angle $a=38^\circ$ and angle $c=82^\circ$ , what is the value of ?

Possible Answers:

$42^\circ$

$120^\circ$

$60^\circ$

$52^\circ$

$60^\circ$

Correct answer:

$60^\circ$

Explanation:

For this problem, remember that the sum of the degrees in a triangle is $180^\circ$ .

This means that $a+b+c=180^\circ$ .

Plug in our given values to solve:

$38^\circ+b+82^\circ=180^\circ$

$120^\circ+b=180^\circ$

$c=60^\circ$

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Example Question #52 : Triangles

In $\Delta ABC$ , AB = 26 , BC = 51 , and AC = 23 . To the nearest tenth, what is $m \angle A$ ?

Possible Answers:

A triangle with these sidelengths cannot exist.

$153.5^{\circ }$

$158.5^{\circ }$

$168.5^{\circ }$

$148.5^{\circ }$

Correct answer:

A triangle with these sidelengths cannot exist.

Explanation:

The sum of the two smallest sides is less than the greatest side:

26 + 23 = 49 < 51

By the Triangle Inequality, this triangle cannot exist.

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Example Question #53 : Triangles

Exterior_angle

If the measure of $\angle A=52^{\circ}$ and the measure of $\angle B= 43^{\circ}$ then what is the meausre of $\angle\theta$ ?

Possible Answers:

$85^{\circ}$

$82^{\circ}$

$95^{\circ}$

Not enough information to solve

$98^{\circ}$

Correct answer:

$95^{\circ}$

Explanation:

The key to solving this problem lies in the geometric fact that a triangle possesses a total of $180^{\circ}$ between its interior angles. Therefore, one can calculate the measure of $\angle C$ and then find the measure of its supplementary angle, $\angle\theta$ .

$180^{\circ}=\angle A + \angle B + \angle C$

$\angle C= 180^{\circ}- 52^{\circ} - 43^{\circ}$

$\angle C= 85^{\circ}$

$\angle C$ and $\angle\theta$ are supplementary, meaning they form a line with a measure of $180^{\circ}$ .

$\angle\theta =180^{\circ} - 85^{\circ}$

$\rightarrow 95^{\circ}$

One could also solve this problem with the knowledge that the sum of the exterior angle of a triangle is equal to the sum of the two interior angles opposite of it.

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Example Question #54 : Triangles

Exterior_angle

If the measure of $\angle A=56^{\circ}$ and the measure of $\angle B=47^{\circ}$ then what is the meausre of $\angle\theta$ ?

Possible Answers:

$87^{\circ}$

Not enough information to solve

$107^{\circ}$

$77^{\circ}$

$103^{\circ}$

Correct answer:

$103^{\circ}$

Explanation:

$180^{\circ}=\angle A + \angle B + \angle C$

$\angle C= 180^{\circ}- 56^{\circ} - 47^{\circ}$

$\angle C=77^{\circ}$

$\angle C$ and $\angle\theta$ are supplementary, meaning they form a line with a measure of $180^{\circ}$ .

$\angle\theta =180^{\circ} - 77^{\circ}$

$\rightarrow 103^{\circ}$

One could also solve this problem with the knowledge that the sum of the exterior angle of a triangle is equal to the sum of the two interior angles opposite of it.

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Example Question #21 : How To Find An Angle In An Acute / Obtuse Triangle

A triangle has angles that measure 114 and degrees. What is the measure of its third angle?

Possible Answers:

degrees

120 degrees

degrees

Correct answer:

degrees

Explanation:

The sum of the angles of any triangle is always 180 degrees. Since the third angle will make up the difference between 180 and the sum of the other two angles, add the other two angles together and subtract this sum from 180 .

Sum of the two given angles: 114 + 36 = 150 degrees

Difference between 180 and this sum: 180 - 150 = 30 degrees

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

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°)

Act_math_108_02

B C

Possible Answers:

Correct answer:

Explanation:

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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Example Question #51 : Triangles

You are given a triangle with angles degrees and degrees. What is the measure of the third angle?

Possible Answers:

degrees

Correct answer:

degrees

Explanation:

Recall that the sum of the angles of a triangle is 180 degrees. Since we are given two angles, we can then find the third. Call our missing angle .

60 + 80 + x = 180

We combine the like terms on the left.

140 + x = 180

Subtract 140 from both sides.

x = 40

Thus, we have that our missing angle is degrees.

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Example Question #51 : Triangles

What is the third angle in a triangle with angles of 120 degrees and degrees?

Possible Answers:

degrees

No such triangle can exist.

degrees

Correct answer:

No such triangle can exist.

Explanation:

We know that the sum of the angles of a triangle must add up to 180 degrees. The two given angles sum to 190 degrees. Thus, a triangle cannot be formed.

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Example Question #171 : Act Math

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

Screen_shot_2013-03-18_at_3.27.08_pm

Possible Answers:

50°

60°

70°

80°

Correct answer:

50°

Explanation:

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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High School Math : Triangles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Acute / Obtuse Triangles

Example Question #51 : Triangles

Example Question #52 : Triangles

Example Question #53 : Triangles

Example Question #54 : Triangles

Example Question #21 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #51 : Triangles

Example Question #51 : Triangles

Example Question #171 : Act Math

All High School Math Resources

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