Question

40 points. Given: Two congruent angles ∠C and ∠R are supplementary. Prove: ∠R and ∠C are both right angles. It doesn't have to be exactly 10 rows.

Statements Reasons
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Answer 1

The proof is explained step-wise below :

Explanation:

Given : ∠C and ∠R are supplementary. Also, ∠C and ∠R are congruent

To Prove : ∠C and ∠R are right angles ⇒ ∠C = ∠R = 90°

Proof : Given ∠C and ∠R are congruent and the congruent angles are equal in measure.

⇒ m∠C = m∠R .........(1)

Now, ∠C and ∠R are supplementary

⇒ ∠C + ∠R = 180°

⇒ ∠C + ∠C = 180° ( From equation (1) )

⇒ 2∠C = 180°

⇒ ∠C = 90°

Hence, ∠C = ∠R = 90°

⇒ ∠C and ∠R both are right angles.

Hence Proved.