Question

How many sides does a polygon have if the sum of the measures of its internal angle is five times as large as the sum of the measure of its exterior angles?

Answer 1

HINT:-To solve this question, we must know the following formula:-
Sum of the measure of the interior angles of a regular polygon = (n – 2)180
Where, ‘n’ = the number of sides of a regular polygon.
Also, we must know that the sum of the exterior angles of a regular polygon always add up to 360°.

Complete step-by-step answer:
Let us now solve this question.
The sum of the measure of the interior angles of a regular polygon is calculated as (n – 2) 180, where ‘n’ = the number of sides of a regular polygon.
According to the question,
The sum of the measures of the internal or interior angles of a polygon is five times the sum of the measure of its exterior angles. Therefore:-
(n − 2) 180 = 5 (360)
$\Rightarrow $ 180n – 360 = 1800
$\Rightarrow $ 180n = 1800 + 360
$\Rightarrow $ 180n = 2160
$\Rightarrow $ n = \[\dfrac{2160}{180}\]
$\Rightarrow $ n = 12

NOTE: Students should know that the sum of exterior angles is always 360° but the sum of interior angles depends on the number of sides of the polygon. Students may be confused about interior or exterior angles.