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

72^o

100^o

120^o

144^o

Correct answer is D

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

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