Question

If m∠ QOS=58, m∠ POR=61, and m∠ POQ=22 what is m∠ ROS

Answer 1

∠ROS = 19

Explanation:

The angle sum theorem is applicable.

∠POQ + ∠QOR = ∠POR

∠QOR = ∠POR - ∠POQ . . . . . subtract ∠POQ

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∠QOR +∠ROS = ∠QOS

∠ROS = ∠QOS - ∠QOR . . . . . subtract ∠QOR

∠ROS = ∠QOS - (∠POR - ∠POQ) . . . . . substitute for ∠QOR

∠ROS = ∠QOS - ∠POR + ∠POQ = 58 -61 +22

∠ROS = 19