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Offline Centres

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

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106 °

156 °

126 °

136 °

answer is C.

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Detailed Solution

Concept: Line is a straight line between two points. To find the angle of the given data we are using lines and angles.
In given figure,

∠ POY = 90 °

∠ POX + ∠ POY = 180 °

∠ POX + 90 ° = 180 °

= ∠ POX = 90 °

Given:

a : b = 2 : 3

Now, let

a = 2 x

b = 3 x

Therefore,

∠ POX = a + b

∠ POX = 2 x + 3 x

∠ POX = 5 x

Then,

90 ° = 5 x

= x = 18 °

Now,

∠ MOX = b = 3 x

= ∠ MOX = 3 x = 3 \times 18

∠ MOX = 54 °

Then,

∠ MOX + ∠ NOX = 180 °

b + c = 180 °

54 ° + c = 180 °

c = 126 °

Hence, the correct answer is 3.

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