. In the given figure, SO and RO are the bisectors
of PSR and QRS respectively. If PSR = QRS
60°, and
SPQ 100°, find the measure of
SOR and PQR.
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Answer:
<PQR=140 degrees and <SOR=120 degrees
Step-by-step explanation:
It is given that OR and OS bisect angles QRS and PSR respectively. Now, considering triangle ROS we have, <ORS = 30 and < OSR = 30. Since the angle sum property of a triangle states that sum of all angles in a triangle must add up to 180, we get <SOR=120 degrees [180-(30+30)=120].
Now, considering the quadrilateral PQRS, the angle sum should be 360, and we know <PSR=60, <QRS=60 and <SPQ=100. Hence, <PQR=140 [360-(100+60+60)=140].
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