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Example 3 - OP, OQ, OR and OS are four rays. Prove that - Angles - Problems


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Example 3 In figure, OP, OQ, OR and OS are four rays. Prove that ∠ POQ + ∠ QOR + ∠ SOR + ∠ POS = 360°. Lets extend ray PQ backwards till T Now, ∠TOP + ∠POQ = 180° Also, ∠TOS + ∠ SOR + ∠ QOR = 180° Adding (1) & (2) ∠ TOP + ∠ POQ + ∠ TOS + ∠ SOR + ∠ QOR = 360° But ∠ TOP + ∠ TOS = ∠ POS ∠ POQ + ∠ QOR + ∠ SOR + ∠ POS = 360 ° ∠ POQ + ∠ QOR + ∠ SOR + ∠ POS = 360 ° Hence Proved.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.
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