Question

∠s and ∠q are supplementary and ∠q and ∠r are supplementary. complete the proof that ∠s ≅ ∠r.

	statement	reason
2	∠q and ∠r are supplementary	given
3	( mangle s + mangle q = 180^circ )	definition of supplementary angles
4	( mangle q + mangle r = 180^circ )
5	( mangle s + mangle q = mangle q + mangle r )	transitive property of equality
6	( mangle s = mangle r )	properties of addition, subtraction, multiplication, and division
7	( angle s cong angle r )	definition of congruence

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Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose measures add up to \(180^\circ\). So, if \(\angle Q\) and \(\angle R\) are supplementary, by the definition of supplementary angles, we have \(m\angle Q + m\angle R = 180^\circ\).

Answer:

Definition of supplementary angles