Question

Each angle of a certain regular polygon measures 174°. How many sides does it have?

Answer 1

Remark

Each angle on the interior of a regular polygon has a supplement. All the supplements add up to 360 degrees. For example the exterior angles of a square are all 90o There are 4 of them 4 * 90 = 360o

The enclosed diagram is of a regular octagon. It's interior angles are each 180 - 45 = 135. The 45 is the size of the exterior angles  (360/8) = 45

Solve

Step One

Find the size of the exterior angle of the regular polygon in the given question. Remember the exterior and interior angles are supplementary.

Exterior angle + interior angle = 180

interior angle is given as 174

Exterior angle + 174 = 180

Exterior angle  = 180 - 174 = 6

Step Two

Find the number of exterior angles.

x * 6 = 360  

x = 360/6

x = 60

The number of exterior  angles to this regular polygon is 60

Step Three

Find the number of sides

The number of sides and the number of exterior angles are the same.

The polygon with interior angles = 174 has 60 sides. <<<< Answer