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

Solution

∵ XOY is a line
∴ b + a + 90° = 180°

$rightwards double arrow$ a + b = 90⁰
2 + 3 = 5
$therefore space space space space space space angle straight a equals 2 over 5 cross times 90 degree equals 36 degree space space space space space space space space angle straight b space equals space 3 over 5 cross times 90 degree equals 54 degree because space space space space MON space is space straight a space line therefore space space space angle straight b plus angle straight c equals 180 degree rightwards double arrow space space space 54 degree plus angle straight c equals 180 degree space rightwards double arrow space angle straight c equals 126 degree$

Some More Questions From Lines and Angles Chapter

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Lines And Angles

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

Some More Questions From Lines and Angles Chapter

In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex angle EOC.

In figure, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

In figure, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.

If the complement of an angle is one-third of its supplement, find the angle.

In figure, find the value of x.

In figure, if ∠POR and ∠QOR form a linear pair and a - b = 80° then find the value of a and b.

What value of x would make XOY a line if ∠XOZ = 7x + 20° and ∠YOZ = 3x in figure.

Two supplementary angles are in the ratio 4 : 5. Find the angles.

In figure, lines AB and CD intersect at O. If ∠AOD : ∠DOC = 4 : 5 then find ∠COB.

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