Question

All sides of a regular pentagon are extended to form a star with vertices P,Q,R,S,T. What is the sum of the angles made at the vertices?___

Answer 1

Interior angle = [(2n-4)x90]/n = 108

2x= 360-(108x2) = 144

angle P = 180-144= 36

Total = 36x5= 180

Useful to remember: Sum of angles in a star= 180${}^{\circ }$

Shortcut: Clearly the star point trisects the angle in a pentagon. Hence each angle = 108/3 = 36.

Sum of angles = 36*5 = 180

Alternatively: Sum of angles of a n point star = (n – 4) x 180${}^{\circ }$ , where n = number of sides of a polygon.

Here, n = 5. Sum of angles of a n point star = (5 – 4) x 180${}^{\circ }$ = 180${}^{\circ }$.