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

### Question

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

### 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 2xo, 3xo respectively. Thus 2xo + 3xo + 3 x 60 = 3x sum of angles of $$\Delta$$a

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

5xo + 180o = 540o

5xo = 540o - 180o

5xo = 360o

xo = $$\frac{360^o}{5}$$

= 72o

Hence, the smaller of the two angles is

2 x 72o = 144o

## Dicussion (1)

• 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 2xo, 3xo respectively. Thus 2xo + 3xo + 3 x 60 = 3x sum of angles of $$\Delta$$a

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

5xo + 180o = 540o

5xo = 540o - 180o

5xo = 360o

xo = $$\frac{360^o}{5}$$

= 72o

Hence, the smaller of the two angles is

2 x 72o = 144o