### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Pentagons

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

**Possible Answers:**

This pentagon cannot exist.

**Correct answer:**

This pentagon cannot exist.

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 ?

**Possible Answers:**

This pentagon cannot exist.

**Correct answer:**

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 ?

**Possible Answers:**

This pentagon cannot exist.

**Correct answer:**

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

If , then the above becomes:

### Example Question #4 : How To Find An Angle In A Pentagon

Solve for :

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of a pentagon can be determined by the following equation, where is the number of sides:

Therefore: