Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles

A. 72o
B. 100o
C. 120o
D. 144o

Correct Answer: Option D

D. 144o

The diagram given simple illustrates that a pentagon contains three Δs.

Two angles which are in the ratio 2:3 will have actual values 2xo, 3xo respectively. Thus 2xo + 3xo + 3 x 60 = 3x sum of angles of Δa

i.e. 5xo + 180o = 3 x 180o

5xo + 180o = 540o

5xo = 540o – 180o

5xo = 360o

xo = 360o5

= 72o

Hence, the smaller of the two angles is

2 x 72o = 144o