Question

Given: angle 1 is supplementary to angle 2 and angle 1 is congruent to angle 3.

Answer 1

 ∠1 and ∠2 are supplementary    // given∠3 and ∠4 are supplementary    // given∠1 ≅ ∠3    // given m∠1 + m∠2 = 180°    // definition of supplementary anglesm∠3 + m∠4 = 180°    // definition of supplementary angles m∠1 + m∠2 = m∠3 + m∠4    // transitive property of equality m∠1 = m∠3    // definition of congruent angles m∠1 + m∠2 = m∠1 + m∠4    // substitution property of equality (replaced m∠3 with m∠1) m∠2 = m∠4    // subtraction property of equality (subtracted m∠1 from both sides) ∠2 ≅ ∠4    // definition of congruent angles