Question

In this fig lines XY and MN intersects at O. If angle POY =90degree and a ratio b=2 ratio 3,find c​

Answer 1

Answer:

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Answer 2

AnswEr:

We have,

$\qquad$ $\sf{a:b=2:3}$

So, let a = 2x and b = 3x

Clearly, ray OP stands on line XY

$\therefore \qquad \sf \angle \: XOP + \angle \: POY = 180 \degree \\ \\ \\ \colon \implies \sf \: a + b + 90 \degree = 180 \degree \\ \\ \\ \colon \implies \sf a + b = 90 \degree \\ \\ \\ \colon \implies \sf \: 2x + 3x = 180 \degree \\ \\ \\ \colon \implies \sf \:5x = 90 \degree \\ \\ \\ \colon \implies \sf \: x = \cancel \frac {90}{5} \\ \\ \\ \colon \implies \sf\orange{\: x = 18 \degree}$

Since ray OX stands on line MN.

$\\ \therefore \qquad \sf \angle \: MOX + \angle \: XON = 180 \degree \\ \\ \colon \implies \sf \: b +c = 180 \degree \\ \\ \\ \colon \implies \sf 54 + c \: = 180 \degree \\ \\ \\ \colon \implies \sf \blue{c = 126 \degree}$