Question

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complete the proof that m∠rut + m∠qru = 180°. 1 (overleftrightarrow{tv}paralleloverleftrightarrow{qs}) given 2 ∠rut ≅ ∠prq corresponding angles theorem 3 m∠prq + m∠qru = 180° angles forming a linear pair sum to 180° 4 m∠rut + m∠qru = 180° properties of addition, subtraction, multiplication, and division reflexive property of congruence reflexive property of equality substitution transitive property of congruence transitive property of equality

Explanation:

Step1: Analyze given equal - angle relationship

We know from step 2 that $\angle{RUT}\cong\angle{PRQ}$, which means $m\angle{RUT}=m\angle{PRQ}$ (since congruent angles have equal measures).

Step2: Consider the linear - pair equation

In step 3, we have $m\angle{PRQ}+m\angle{QRU} = 180^{\circ}$.

Step3: Substitute equal angle measures

Since $m\angle{RUT}=m\angle{PRQ}$, we can substitute $m\angle{RUT}$ for $m\angle{PRQ}$ in the equation $m\angle{PRQ}+m\angle{QRU} = 180^{\circ}$. So we get $m\angle{RUT}+m\angle{QRU}=180^{\circ}$.

Answer:

Substitution