Question

complete the proof that m∠uty + m∠rwx = 180°. 1. vx || hj given 2. su || hj given 3. ∠rwx ≅ ∠jir corresponding angles theorem 4. m∠jir + m∠uty = 180° same - side interior angles theorem 5. m∠uty + m∠rwx = 180° reflexive property of congruence reflexive property of equality substitution transitive property of congruence transitive property of equality

Explanation:

Step1: Recall angle - congruence and equality properties

We know from step 3 that $\angle RWX\cong\angle JIR$, which means $m\angle RWX = m\angle JIR$.

Step2: Substitute equal - angle measures

In step 4, we have $m\angle JIR + m\angle UTY=180^{\circ}$. Since $m\angle RWX = m\angle JIR$, we can substitute $m\angle RWX$ for $m\angle JIR$ in the equation $m\angle JIR + m\angle UTY = 180^{\circ}$.

Answer:

Substitution