Question

Pls solve
All angles
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Answer 1

Answer:

given: since PQRS is a rectangle, therefore, PS||RQ, PQ||SR, angle POQ is 110°

To find: i.angle PQO

ii.anglePSQ

iii.angle ORS

Solution: i. we are given angle POQ is 110°

thus, according to angle sum property, angle PQO+OPQ=180°-110°

thus, angles POQ+OPQ=70°

now, SR||PQ

thus, angles POQ and OPQ are adjacent angles and adjacent angles are equal

therefore, angle POQ=angle OPQ=35°

ii. angle POQ=35° (proved above)

angles POQ and PSQ are co interior angles(SR||PQ)and co interior angles sum upto 180°

thus, angle PSQ=180°-angle POQ

=180°-35°

angle PSQ=145°

iii. SR||PQ(given)

thus, angles QPO=ORS (alternate interior angles)

now, angle QPO=35°(proved above)

therefore, angle ORS=35°