how many sides does a regular polygon have if each interior angle measures 168°?
how many sides does a regular polygon have if each interior angle measures 168°?
Answer
Explanation:
Step1: Find the measure of each exterior angle
The sum of an interior angle and its corresponding exterior angle of a polygon is (180^{\circ}). If the interior angle is (168^{\circ}), then the exterior angle (e = 180^{\circ}-168^{\circ}=12^{\circ})
Step2: Use the formula for the measure of an exterior angle of a regular polygon
The formula for the measure of an exterior angle (e) of a regular polygon with (n) sides is (e=\frac{360^{\circ}}{n}) We know (e = 12^{\circ}), so (n=\frac{360^{\circ}}{e}) Substitute (e = 12^{\circ}) into the formula: (n=\frac{360^{\circ}}{12^{\circ}} = 30)
Answer:
The regular polygon has (30) sides.