Question

In the figure below, two straight line PQ and RS intersect each other at O. If <POT = 65°. Find values of a,b and c respectively?​

Answer 1

Angles 75, a, b lie on a straight line.

Hence, 75 + a + b = 180

a + b = 105.

4 b and a are vertically opposite angles. Hence,

4 b = a

Substitute this value of a in the above equation.

a + b = 105.

4 b + b = 105

5 b = 105

b = 21.

Substitute b value in 4 b = a

4 * 21 = a

a = 84

Angles around a point sum up to 360.

2 c + a + b + 75 + 4 b = 360

Substituting the values of a and b

2 c + 84 + 21 + 75 + 4 * 21 = 360

2 c + 264 = 360

2 c = 96

c = 48

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