Question

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Congruent Angle pairs

Answer 1

Option A ∠RWQ, ∠WPS and ∠PWU

Explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

Part 1)

∠OPW+∠WPS=180° ------> by supplementary angles

we have

∠OPW=110°

substitute

110°+∠WPS=180°

∠WPS=180°-110°=70°

Part 2) we know that

∠RWQ+(50°+60°)=180° ------> form a linear pair

∠RWQ=180°-(50°+60°)=70°

so

∠OPW+∠RWQ=180° -----> by supplementary angles

Part 3) we know that

∠PWU=∠RWQ -------> by vertical angles

so

∠OPW+∠PWU=180° -----> by supplementary angles

therefore

The angles that are supplements to angle ∠OPW are

∠WPS, ∠RWQ and ∠PWU