### All High School Math Resources

## Example Questions

### Example Question #271 : Plane Geometry

An isosceles triangle has a base of and an area of . What must be the height of this triangle?

**Possible Answers:**

**Correct answer:**

.

### Example Question #1 : Isosceles Triangles

One side of an acute isosceles triangle is 15 feet. Another side is 5 feet. What is the perimeter of the triangle in feet?

**Possible Answers:**

**Correct answer:**

Because this is an acute isosceles triangle, the third side must be the same as the longer of the sides that you were given. To find the perimeter, multiply the longer side by 2 and add the shorter side.

### Example Question #2 : 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 #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

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:**

20°

25°

30°

Cannot be determined from the given information

15°

**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 #1 : 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:**

None of the other answers

140 degrees

40 degrees

70 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 #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

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

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

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

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 #1 : Acute / Obtuse 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 :