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
<em><u>Step One</u></em>
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
<em><u>Step Two</u></em>
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
<em><u>Step Three</u></em>
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
