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

Question

In Fig. 8.47, lines PQ and RS intersect each other at point O . If &#x2220; POR : &#x2220; ROQ = 5 : 7, find all the angles.

Philoid · Accepted Answer

Given,

∠POR and ∠ROP is linear pair

∠POR + ∠ROP = 180^o

Given that,

∠POR = ∠ROP = 5: 1

Therefore,

∠POR = * 180^o = 75^o

Similarly,

∠ROQ = 105^o

Now,

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

Therefore,

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

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