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?

• A. 240
• B. 180
• C. 175
• D. 160

Answer 1

The correct option is B 180

option b

Interior angle = $\frac{\left[\right(2n-4\left)x90\right]}{n}$ = 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 = $\frac{108}{3}$ = 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${}^{\circ }$.