Question

In the given figure, two straight lines PQ and RS intersect at O. If Z POS = 114º, find the measure of each of the angles : (i) \_ POR (ii) \_ROQ (iii) \_QOS​

Answer 1

Answer:

We know vertically opposite angles are equal,

So, ∠POS = ∠ROQ = 114°

and, ∠POR = ∠QOS = x (suppose)

then,

∠POS + ∠ROQ + ∠POR + ∠QOS = 360°

Putting the values,

114° + 114° + x + x =  360°

or, 2x =  360° - 228° = 132°

or, x = 132°/2 = 66°

So,

Required angles are:

∠POS = ∠ROQ = 114°

∠POR = ∠QOS = 66°