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

Explanation

The diagram given simple illustrates that a pentagon contains three \(\Delta\)s.

Two angles which are in the ratio 2:3 will have actual values 2x^o, 3x^o respectively. Thus 2x^o + 3x^o + 3 x 60 = 3x sum of angles of \(\Delta\)a

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

5x^o + 180^o = 540^o

5x^o = 540^o - 180^o

5x^o = 360^o

x^o = \(\frac{360^o}{5}\)

= 72^o

Hence, the smaller of the two angles is

2 x 72^o = 144^o