Polygon Sum Interior & Exterior Angles Review

What is the sum of the measures of the interior angles of an octagon?

Answer explanation

(8 - 2)*180 = 1080

What is the sum of the measures of the interior angles of a 25-gon?

Answer explanation

(25 - 2)*180 = 4140

What is the measure of each interior angle of a regular hexagon?

Answer explanation

Sum of interior angles for a hexagon is 720.

To find one, you do sum/# of angles.

So,

720/6 = 120

What is the measure of each interior angle of a regular 16-gon?

Answer explanation

Sum of interior angles for a 16-gon is 2520.

To find one, you do sum/# of angles.

So,

2520/16 = 157.5

What is the sum of the measures of the exterior angles of a decagon?

What is the measure of each exterior angle of a regular 30-gon?

Answer explanation

Sum of exterior/# of angles

Sum of exterior angles is always 360!

360/30 = 12

If the exterior angle of a regular polygon is 22.5^o, how many sides does it have?

Answer explanation

Sum of exterior/exterior angle measure

360/22.5 = 16

If the interior angle of a regular polygon is 170^o, how many sides does the polygon have?

Answer explanation

Find the exterior angle, 180 - 170 = 10.

Take the sum of the exterior angles and divide by the measure of the exterior angle.

360/10 = 36 sides

If the sum of the interior angle measures is 1980^o, how many sides does the polygon have?

If the sum of the interior angle measures is 5400^o, how many sides does the polygon have?