Question

complete the proof that (mangle utw + mangle twx = 180^{circ}).
statement reason
1 (overleftrightarrow{vx}paralleloverleftrightarrow{su}) given
2 (angle twxcongangle rtu) corresponding angles theorem
3 (mangle rtu + mangle utv = 180^{circ}) angles forming a linear - pair sum to (180^{circ})
4 (mangle utw + mangle twx = 180^{circ})

Explanation:

Step1: Given parallel lines

$\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$

Step2: Use corresponding - angles theorem

Since $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$, $\angle TWX\cong\angle RTU$ (Corresponding Angles Theorem)

Step3: Recognize linear - pair property

$\angle RTU$ and $\angle UTV$ form a linear pair, so $m\angle RTU + m\angle UTV=180^{\circ}$

Step4: Substitute equal angles

Since $\angle TWX\cong\angle RTU$, we can substitute $\angle RTU$ with $\angle TWX$ in the equation $m\angle RTU + m\angle UTV = 180^{\circ}$. So $m\angle UTW + m\angle TWX=180^{\circ}$ (Substitution Property of Equality)

Answer:

Substitution Property of Equality