27.In the given figure , lines PQ and RS intersect each other at point O. If angle POR : angle ROQ is 5:15. Then find the value of the angle SOQ. *
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SOQ = 100°
Step-by-step explanation:
Given: PQ and RS intersect each other at O.
POR:ROQ = 5:15
To find: Angle SOQ
Let the ratio between them be as x...
POR + ROQ = 180° [Linear pair, lie on a straight line]
Therefore,
5x + 15x = 180°
20x = 180°
x = 180/ 20
x = 90°
Therefore,
POR = 5x = 20×5=100°
Since, POR = SOQ [Opposite angles are always equal]
So, Angle SOQ = 100°
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