### All ISEE Upper Level Math Resources

## 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?

**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 #1 : 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 #1 : Pentagons

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 #1 : Pentagons

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:

### Example Question #1 : How To Find The Perimeter Of A Pentagon

Find the perimeter of a pentagon with a side of length 12in.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a pentagon, we will use the following formula:

where *a* is the length of one side of the pentagon.

Now, we know the length of one side of the pentagon is 12in.

Knowing this, we can substitute into the formula. We get

### Example Question #2 : How To Find The Perimeter Of A Pentagon

Find the perimeter of a pentagon with a side having a length of 21in.

**Possible Answers:**

**Correct answer:**

A pentagon has 5 sides. To find the perimeter, we will use the following formula:

where *a* is the length of a side of the pentagon.

Now, we know the length of a side of the pentagon is 21in.

Knowing this, we will substitute into the formula. We get

### Example Question #1 : How To Find The Perimeter Of A Pentagon

Find the perimeter of a pentagon with a side having a length of 15cm.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a pentagon, we will use the following formula:

where *a* is the length of one side of the pentagon. Because a pentagon has 5 equal sides, we can use any side in the formula.

So, we know the length of one side of the pentagon is 15cm. So, we can substitute. We get

### Example Question #122 : Plane Geometry

A pentagon has a side of length 11in. Find the perimeter.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a pentagon, we will use the following formula:

where *a* is the length of one side of the pentagon.

Now, we know the length of one side of the pentagon is 11in.

Knowing this, we can substitute into the formula. We get

### Example Question #5 : How To Find The Perimeter Of A Pentagon

Find the perimeter of a pentagon with a side having a length of 9in.

**Possible Answers:**

**Correct answer:**

A pentagon has 5 equal sides. To find the perimeter of a pentagon, we will use the following formula:

where *a* is the length of one side of the pentagon.

Now, we know a side of the pentagon has a length of 9in. So, we get

### Example Question #1 : How To Find The Length Of The Side Of A Pentagon

In a pentagon in which all the angles are equal and the perimeter is 35 inches, how many inches would be the sum of 2 of the sides?

**Possible Answers:**

**Correct answer:**

In a pentagon in which all angles are equal, all sides will also be equal; therefore, the length of one side can be found by dividing the perimeter by 5 (the number of sides in a pentagon). Given that , the sum of 2 of the sides will be