Question

if ∠a is supplementary to ∠b and ∠c is supplementary to ∠b then ∠a ≅ ∠c

Explanation:

Step1: Recall the definition of supplementary angles

If \(\angle A\) is supplementary to \(\angle B\), then \(m\angle A + m\angle B=180^{\circ}\). If \(\angle C\) is supplementary to \(\angle B\), then \(m\angle C + m\angle B = 180^{\circ}\).

Step2: Use the congruent supplements theorem

The congruent supplements theorem states that if two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent. Here, \(\angle A\) and \(\angle C\) are both supplementary to \(\angle B\).

Answer:

Congruent Supplements Theorem