If ∠A ≅ ∠B, then which statement about supplements is true?

If ∠A ≅ ∠B, then which statement about supplements is true?

• A. If ∠A ≅ ∠B, then ∠A and ∠B are supplements.
• B. If ∠A ≅ ∠B, then the supplements of ∠A and ∠B are congruent.
• C. If ∠A ≅ ∠B, then ∠A and ∠B are congruent complements.
• D. If ∠A ≅ ∠B, then the supplements of ∠A and ∠B are supplementary.

Answer: (B)

When two angles are congruent, they have equal measures. The supplement of an angle is the angle that adds to 180 degrees with it, so its measure is 180 minus the angle’s measure. If ∠A ≅ ∠B, then m∠A = m∠B. The supplement of ∠A has measure 180 − m∠A, and the supplement of ∠B has measure 180 − m∠B. Since m∠A = m∠B, these two supplements have the same measure, so they are congruent. That’s why the valid statement is that the supplements of ∠A and ∠B are congruent. The other options aren’t guaranteed: two congruent angles aren’t necessarily supplements to each other, so the first can fail. Being congruent complements would require a specific relationship to 90 degrees that isn’t given. And the supplements of ∠A and ∠B aren’t guaranteed to be supplementary to each other unless the original angles are 90 degrees.

When two angles are congruent, they have equal measures. The supplement of an angle is the angle that adds to 180 degrees with it, so its measure is 180 minus the angle’s measure. If ∠A ≅ ∠B, then m∠A = m∠B. The supplement of ∠A has measure 180 − m∠A, and the supplement of ∠B has measure 180 − m∠B. Since m∠A = m∠B, these two supplements have the same measure, so they are congruent. That’s why the valid statement is that the supplements of ∠A and ∠B are congruent.

The other options aren’t guaranteed: two congruent angles aren’t necessarily supplements to each other, so the first can fail. Being congruent complements would require a specific relationship to 90 degrees that isn’t given. And the supplements of ∠A and ∠B aren’t guaranteed to be supplementary to each other unless the original angles are 90 degrees.