In Fig. 6.14, lines XY and MN intersect at O. If∠ POY = 90° and a: b = 2 : 3, find c.

Question

In Fig. 6.14, lines XY and MN intersect at O. If &#x2220; POY = 90&#xB0; and a: b = 2 : 3, find c.

Philoid · Accepted Answer

It is given in the question that:

∠POY = 90^O

And,

a : b = 2 : 3

Now, according to the question,

∠POY + a + b = 180^o

90^o + a + b = 180^o

a + b = 90^o

Let a be 2x and b as 3x

2x + 3x = 90^o

5x = 90^o

x = 18^o

Hence,

a = 2 * 18^o = 36^o

And,

b = 3 * 18^o = 54^o

And,

b + c = 180^o (Linear pair)

54^o + c = 180^o

c = 126^o