# ISEE Upper Level Math : How to find an angle in a pentagon

## Example Questions

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

A convex pentagon has four angles that measure  each. What is the measure of the fifth angle?

This pentagon cannot exist.

This pentagon cannot exist.

Explanation:

The angles of a pentagon measure a total of . If we let the unknown angle measure be , then from this information:

Since an angle measure cannot be negative, this pentagon cannot exist.

### Example Question #2 : How To Find An Angle In A Pentagon

The measures of the angles of a pentagon are . If , what is ?

This pentagon cannot exist.

Explanation:

The angles of a pentagon measure a total of . From the information, we know that:

If , then

### Example Question #3 : How To Find An Angle In A Pentagon

The measures of the angles of a pentagon are . If , what is ?

This pentagon cannot exist.

Explanation:

The angles of a pentagon measure a total of . From the information, we know:

If , then the above becomes:

Solve for :