### All High School Math Resources

## Example Questions

### Example Question #1 : Isosceles 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:**

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 #2 : 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:**

30°

20°

15°

Cannot be determined from the given information

25°

**Correct answer:**

20°

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

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

**Possible Answers:**

140 degrees

70 degrees

None of the other answers

40 degrees

100 degrees

**Correct answer:**

70 degrees

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 #3 : Isosceles Triangles

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

**Possible Answers:**

**Correct answer:**

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 #4 : Isosceles 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:**

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 #5 : Triangles

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

**Possible Answers:**

**Correct answer:**

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 #1 : Acute / Obtuse Isosceles 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:**

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 #6 : Isosceles 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:**

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:**

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 #1 : 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:**

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 .