### All ACT Math Resources

## Example Questions

### Example Question #31 : Plane Geometry

The figure above is a pentagon. All of the angles listed (except the interior one) are exterior angles to the pentagon's interior angles.

What is the value of in the figure above?

**Possible Answers:**

**Correct answer:**

There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:

, where is the number of sides.

Therefore, a hexagon like this one has:

.

Next, you should remember that all of the exterior angles listed are supplementary to their correlative interior angles. This lets you draw the following figure:

Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to . Thus, you can write:

Solve for :

### Example Question #1 : How To Find An Angle In A Pentagon

The figure above is a pentagon. All of the angles listed (except the interior one) are exterior angles to the pentagon's interior angles.

What is the value of the largest unknown angle in the figure above?

**Possible Answers:**

**Correct answer:**

There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:

, where is the number of sides.

Therefore, a hexagon like this one has:

.

Next, you should remember that all of the exterior angles listed are supplementary to their correlative interior angles. This lets you draw the following figure:

Now, you just have to manage your algebra well. You must sum up all of the interior angles and set them equal to . Thus, you can write:

Solve for :

Now, you have to find the *largest* unknown angle, which is :

### Example Question #32 : Plane Geometry

What is the sum of three angles in a pentagon?

**Possible Answers:**

**Correct answer:**

The sum of all angles is determined by the following formula for a polygon:

In a pentagon, there are 5 sides, or . Substitute and find the total possible angle in a pentagon.

There are 5 interior angles in a pentagon. Divide the total possible angle by 5 to determine the value of one interior angle.

Each interior angle of a pentagon is 108 degrees.

The sum of three angles in a pentagon is:

Certified Tutor