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Question

# In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.

A

180

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B

90

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C

120

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D

75

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Solution

## The correct option is B 90∘ Here, ∠POS and ∠SOQ are adjacent angles with non common arms OP and OQ forming a line. ⇒∠POS + ∠SOQ = 180∘ (Linear pair) ∠POS = x (Given) ⇒ x + ∠SOQ = 180∘ ⇒ ∠SOQ = 180∘ – x Now, ray OR bisects ∠POS. ⇒ ∠ROS = 12 × ∠POS ⇒ ∠ROS=x2 Similarly, ∠SOT=12 × ∠SOQ ⇒ ∠SOT=12 × ( 180∘ - x) ⇒ ∠SOT=90∘ – x2 ⇒∠ROT = ∠ROS + ∠SOT ⇒∠ROT = x2 + 90∘ – x2 ⇒∠ROT= 90∘

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