Q18 of 115 Page 8

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

Given,

∠POR and ∠ROP is linear pair


∠POR + ∠ROP = 180o


Given that,


∠POR = ∠ROP = 5: 1


Therefore,


∠POR = * 180o = 75o


Similarly,


∠ROQ = 105o


Now,


∠POS = ∠ROQ = 105o(Vertically opposite angles)


Therefore,


∠SOQ = ∠POR = 75o(Vertically opposite angles)


More from this chapter

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16

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

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°


 17

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.

 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.)

 1

In Fig 8.56, lines l1 and l2 intersect at O, forming angles as shown in the figure. If x = 45, find the values of y, z and u.