Q17 of 115 Page 8

In Fig. 8.46, ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠ respectively. If ∠POS = x, find ∠ROT.

Given that,

Ray OS stand on a line POQ


Ray OR and OT are angle bisector of ∠POS and ∠SOQ respectively.


∠POS = x


∠POS + ∠QOS = 180o(Linear pair)


∠QOS = 180o – x


∠ROS = ∠POS (Given)


= x


∠ROS =


Similarly,


∠TOS = (90o - )


Therefore,


∠ROT = ∠ROS + ∠ROT


= + 90o -


= 90o


Therefore, ∠ROT = 90o


More from this chapter

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15

In Fig. 8.44, ∠AOF and ∠FOG form a linear pair.

∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°



(i) Find the measures of ∠FOE, ∠COB and ∠DOE.


(ii) Name all the right angles.


(iii) Name three pairs of adjacent complementary angles.


(iv) Name three pairs of adjacent supplementary angles.


(v) Name three pairs of adjacent angles.

 16

In Fig. 8.45, OP, OQ, OR and OS are four rays, prove that:

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°


 18

In Fig. 8.47, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

 19

In Fig. 8.48, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = (∠QOS –∠POS.)