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

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #3 : Triangles

An isoceles triangle has a base angle five more than twice the vertex angle.  What is the difference between the base angle and the vertex angle?

Possible Answers:

Correct answer:

Explanation:

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

Let = vertex angle and =  base angle

So the equation to solve becomes

or

So the vertex angle is and the base angle is so the difference is

Example Question #1 : Acute / Obtuse Isosceles Triangles

Points A and B lie on a circle centered at Z, where central angle <AZB measures 140°. What is the measure of angle <ZAB?

 

Possible Answers:

25°

20°

Cannot be determined from the given information

30°

15°

Correct answer:

20°

Explanation:

Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation:

140 + 2x = 180 --> 2x = 40 --> x = 20

 

 

 

Example Question #1 : Isosceles Triangles

Triangle FGH has equal lengths for FG and GH; what is the measure of F, if G measures 40 degrees? 

Possible Answers:

40 degrees

100 degrees

70 degrees

None of the other answers

140 degrees

Correct answer:

70 degrees

Explanation:

It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.

Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means F = H, and that F + H + 40 = 180,

By substitution we find that F * 2 = 140 and angle F = 70 degrees. 

Example Question #6 : Triangles

The vertex angle of an isosceles triangle is .  What is the base angle?

Possible Answers:

Correct answer:

Explanation:

An isosceles triangle has two congruent base angles and one vertex angle.  Each triangle contains .  Let  = base angle, so the equation becomes .  Solving for  gives

Example Question #7 : Triangles

In an isosceles triangle the base angle is five less than twice the vertex angle.  What is the sum of the vertex angle and 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  = the vertex angle

and  = base angle

So the equation to solve becomes 

or

Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.

Example Question #161 : Triangles

Sides  and  in this triangle are equal. What is the measure of ?

Triangle_1

Possible Answers:

Correct answer:

Explanation:

This triangle has an angle of . We also know it has another angle of  at  because the two sides are equal. Adding those two angles together gives us  total. Since a triangle has total, we subtract 130 from 180 and get 50.

Example Question #9 : Triangles

An isosceles triangle has a vertex angle that is twenty degrees more than twice the base angle.  What is the sum of the vertex and base angles?

Possible Answers:

40

Correct answer:

Explanation:

All triangles contain degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let and .

So the equation to solve becomes .

We get and , so the sum of the base and vertex angles is .

Example Question #10 : Triangles

If an isosceles triangle has an angle measuring greater than 100 degrees, and another angle with a measuring  degrees, which of the following is true?

Possible Answers:

Correct answer:

Explanation:

In order for a triangle to be an isosceles triangle, it must contain two equivalent angles and one angle that is different. Given that one angle is greater than 100 degrees: Thus, the sum of the other two angles must be less than 80 degrees. If an angle is represented by :

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

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

Possible Answers:

Correct answer:

Explanation:

All triangles have degrees.  An isoceles triangle has one vertex angle and two congruent base angles.

Let vertex angle and  base angle.

So the equation to solve becomes:

or

Thus for the vertex angle and for the base angle.

The sum of the vertex and one base angle is .

Example Question #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An isoceles triangle has a vertex angle that is degrees more than twice the base angle.  What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

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

Let base angle and vertex angle.

So the equation to solve becomes .

 

Thus the base angles are and the vertex angle is .

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