Question

line PQ and RS intersect each other at point O. if angle POR : angle ROQ = 5 : 7, find all the remaining angles.

Answer 1

let angle POR =5X and angle ROQ =7X
Then 5X +7X =180 degree as POQ is a straight angle
so 12X = 180 degree
X = 15 degree
So angle POR =angle QOS=75Degree
and angle ROQ= Angle POS =105 Degree as opposite angles are equal.

Answer 2

According the question line PQ and RS intersect each other at point O. if angle POR : angle ROQ = 5 : 7,

Let consider ∠ POR =5X and ∠ ROQ =7X

∴ 5X +7X =180°                   ( POQ is a straight angle= 180°)

⇒ 12X = 180°

X = 15°

So ∠ POR = 5 ×15 = 75°

Hence ∠POR =∠ QOS=75°           (  opposite angles are equal )

∠ ROQ= 15 × 7 = 105°

Hence ∠ ROQ=∠ POS =105°        ( opposite angles are equal )

∴ ∠ POR =75°

  ∠ QOS=75°  

  ∠ ROQ= 105°

  ∠ POS =105°  

Ans :-  ∠ POR =75°,  ∠ QOS=75° ,∠ ROQ= 105° , ∠ POS =105°  .

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