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In Below Fig, Ray Os Stand on a Line Poq. Ray Or and Ray Ot Are Angle Bisectors of ∠Pos and ∠Soq Respectively. If ∠Pos = X, Find ∠Rot. - Mathematics

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

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Solution

Given,

Ray OS stand on a line POQ

Ray OR and Ray OT are angle bisectors of ÐPOS and ÐSOQ respectively

`∠`POS = x

`∠`POS and `∠`QOS is linear pair

ÐPOS + ÐQOS = 180°

x + ÐQOS = 180°

`∠`QOS = 180 - x

Now, ray or bisector `∠`POS

∴ `∠`ROS = `1/2` `∠`POS

= `1/2`×  x                        [ ∵ `∠`POS = x]

`∠`ROS = x

Similarly ray OT bisector `∠`QOS

 ∵`∠`TOS = `1/2` `∠`QOS

= `180/2` - x                  [∵  `∠`QOS = 180 - x]

=` 90/2` - x

∴ `∠`ROT = `∠`ROS + `∠`ROT

= `x/2`+ 90 -`x/2`

= 90°

∴`∠`ROT = 90°

Concept: Pairs of Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 15 | Page 16

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