A regular polygon has twice the number of sides as another regular polygon. The perimeter of the smaller polygon is 84.8 cm and each of its interior angles measures 140°. The side length of the larger polygon is 1.2 times that of the smaller one. What is the measure of each interior angle of the larger polygon?
160°
Given: the smaller regular polygon has each interior angle 140°, and the larger polygon has twice as many sides.
For the smaller polygon, each exterior angle = \(180° - 140° = 40°\).
Number of sides of the smaller polygon = \(\dfrac{360°}{40°} = 9\).
So the larger polygon has \(2 \times 9 = 18\) sides.
Each interior angle of a regular polygon with n sides = \(\dfrac{(n-2) \times 180°}{n}\).
For the 18-sided polygon: \(\dfrac{(18-2) \times 180°}{18} = \dfrac{16 \times 180°}{18} = \dfrac{2880°}{18} = 160°\).
The perimeter and side-length data are extra information not needed to find the interior angle.
Each interior angle of the larger polygon is 160°.
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