Math 6.1 Review

Example 1

100

A quadrilateral has the interior angle measures of (2x+5)°, x°, x°, and (2x+7)°. Find x.

x=58

200

A pentagon has the interior angle measures of 90, 90, (2x+10), (2x-20), and x. Find x.

x=74

300

Find the measure of x of quadrilateral XYZW with each angle measure being x, 2x, 3x, and 4x. 

x=36

400

A quadrilateral has the interior angle measures of (3x-6)°, (2x-8)°, (x+10)°, and x°. Find x.

x=52

500

A pentagon has the interior angle measures of (3x-11)°, (x+8)°, x°, (2x+7)°, and (x-8)°. Find x.

x=68

Example 2

100

Benjamin is making a model of the Pentagon. He needs to know what the measure of each interior angle. If the Pentagon is a regular shape, what is each measure?

108°

200

Gabriella is making a kid's ride at an amusement park. The design she has ready is in the shape of a regular decagon (10 sides). She needs to know the measure of each interior angle of the shape. What is the measure of each angle?

144°

300

Timothy is designing a stop sign. He needs to know what the measure of each interior angle should be. What is the measure of each interior angle of a regular octagon?

135°

400

Jeffery is remaking the abalone game board. He needs to know the measure of each interior angle of the game board. If the game board is a regular hexagon, what is the measure of each angle?

120°

500

At Tina's new campsite, she is making a campfire with bricks. Each brick adds up to make the shape of a regular octadecagon (18 sides). Tina needs to know the measure of each interior angle to properly construct it. What is the measure of the angles?

160°

Example 3

100

The measure of an interior angle of a regular polygon is 90°. Find the number of sides.

4 sides

200

The measure of an interior angle of a regular polygon is 156°. Find the number of sides.

15 sides

300

The measure of an interior angle of a regular polygon is 135°. Find the number of sides.

8 sides

400

The measure of an interior angle of a regular polygon is 120°. Find the number of sides.

6 sides

500

The measure of an interior angle of a regular polygon is 144°. Find the number of sides.

10 sides

Example 4

100

Find the measure of each exterior angle of a regular quadrilateral.

90°

200

Find the measure of each exterior angle of a regular octagon.

45°

300

The exterior angles of a pentagon are 2x, 52, (x+2), (x+10), and 88. Find x.

x=52

400

The exterior angles of a quadrilateral are 79, (x+10), (x-1), and 2x. Find x.

x=68

500

The exterior angle measures of a hexagon are 2x°, (x+10)°, (x+18)°, 3x°, (x-1)°, and x°. Find x.

x=37