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High School Math : How to find an angle in an acute / obtuse isosceles triangle

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Example Questions

Example Question #11 : Isosceles Triangles

An isoceles triangle has a base angle that is degrees less than three times the vertex angle. What is the product of the vertex angle and the base angle?

Possible Answers:

3375

3750

4500

2250

1875

Correct answer:

2250

Explanation:

Every triangle has 180 degrees. An isoceles triangle has one vertex angle and two congruent base angles.

Let vertex angle and 3x-15= base angle.

Then the equation to solve becomes:

x+(3x-15)+(3x-15)=180 , or 7x-30=180 .

Then the vertex angle is , the base angle is , and the product is 2250 .

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Example Question #11 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?

Possible Answers:

45°

105°

30°

50°

25°

Correct answer:

50°

Explanation:

Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.

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Example Question #166 : Triangles

An isosceles triangle has a base angle that is six more than three times the vertex angle. What is the base angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and 3x + 6 = base angle.

Then the equation to solve becomes

x + (3x + 6) + (3x + 6) = 180

7x + 12 = 180 .

Solving for gives a vertex angle of 24 degrees and a base angle of 78 degrees.

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Example Question #31 : Isosceles Triangles

The base angle of an isosceles triangle is thirteen more than three times the vertex angle. What is the difference between the vertex angle and the base angle?

Possible Answers:

22^o

65^o

79^o

57^o

101^o

Correct answer:

57^o

Explanation:

Every triangle has 180^o . An isosceles triangle has one vertex ange, and two congruent base angles.

Let be the vertex angle and 3x + 13 be the base angle.

The equation to solve becomes x + (3x + 13) + (3x + 13) = 180^o , since the base angle occurs twice.

7x + 26 = 180^o

7x=154^o

x=22^o

Now we can solve for the vertex angle.

3x+13=3(22)+13=79^o

The difference between the vertex angle and the base angle is 79^o - 22^o = 57^o .

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Example Question #284 : Geometry

An isoceles triangle has a base angle that is five less than twice the vertex angle. What is the sum of the base and vertex angles?

Possible Answers:

135

109

Correct answer:

109

Explanation:

Each triangle has 180 degrees.

An isoceles triangle has two congruent base angles and one vertex angle.

Let vertex angle and 2x-5= base angle.

Then the equation to solve becomes x+(2x-5)+(2x-5)=180 or 5x-10=180 .

Add to both sides to get 5x=190 .

Divide both sides by to get x=38 vertex angle and 2x-5=71 base angles, so the sum of the angles is 109 .

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Example Question #285 : Geometry

An isoceles triangle has a base angle that is twice the vertex angle. What is the sum of one base angle and the vertex angle?

Possible Answers:

108

135

Correct answer:

108

Explanation:

Every triangle contains 180 degrees. An isoceles triangle has two congruent base angles and one vertex angle.

Let the vertex angle and 2x = the base angle

So the equation to solve becomes x+2x+2x=180 or 5x=180 and dividing by gives x = 36 for the vertex angle and 2x = 72 for the base angle, so the sum is 108

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High School Math : How to find an angle in an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Isosceles Triangles

Example Question #11 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #166 : Triangles

Example Question #31 : Isosceles Triangles

Example Question #284 : Geometry

Example Question #285 : Geometry

All High School Math Resources

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