Question

in the given figure, two straight lines PQ and RS intersect at a point 0.
If angle POS = 140°, find the measure of each of the angles :
(i) angle POR (ii) angle ROQ (iii) angle QOS​

Answer 1

Step-by-step explanation:

Here,

1) angle POS = 140°.....( given )

so,

angle POR = ?

angle POR + angle POS = 180°...( the sum of 2 corresponding angles is supplementary... it means 180°. )

angle POR + 140° = 180°

angle POR = 180° - 140°...( transforming unnecessary term to a necessary term. )

therefore,

angle POR = 40°....

2). angle ROQ = ?

angle ROQ = angle POS...( vertically opposite angles)

But, angle POS = 140°...( given)

therefore angle ROQ = 140°...

3). angle QOS = ?

As we know now, angle POR = 40° from 2).

angle POR = angle QOS....( vertically opposite angles)

But, angle POR = 40°

therefore,

angle QOS = 40°.

Ans : angle POR= 40°

angle ROQ = 140°

angle QOS= 40°..

Hence proved....

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