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

## Example Questions

### Example Question #1 : Pentagons

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:      ### Example Question #121 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve for :      Explanation:

The sum of the interior angles of a pentagon can be determined by the following equation, where is the number of sides: Therefore:    ### All ISEE Upper Level Math Resources 