UPSC 2015 CDS I Math Paper

Measure of each interior angle of the regular pentagon
=

(5−2)×180°

5

=

540°

5

=108°
∠BCJ = ∠CBF = 108°
∴ ∠ACB = ∠ABC
=180°−108°=72°
Using angle sum property in ABC,we have
∠A=180°−(∠ACB+∠ABC)
=180°−(72°+72°)
=180°−144=36°
Thus, the measure of each angle at the angular points of the star figure is 36°.
Formula :Each interior angle of the regular polygon of side
n=

(n−2)×180°

n