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
