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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

Options

A) 72o

B) 100o

C) 120o

D) 144o


The correct answer is D.

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


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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

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