Question

Find the measure of angle x in the polygon given below if each side and the interior angle in the polygon measures the same.
(3 marks)

Answer 1

The sum of all the interior angles of an ‘n’ sided polygon = (n - 2) × ${180}^{\circ }$
(1 mark)
Here, number of sides = 5
Therefore, sum of the interior angles = (5-2)× ${180}^{\circ }$
= 3 × ${180}^{\circ }$
= ${540}^{\circ }$
(1 mark)
x is the measure of one of the interior angles of the pentagon.
Since it is a pentagon with each side and interior angle equal, so we conclude that each angle = x
= 540/5
= ${108}^{\circ }$
(1 mark)