Question

the two - column proof below describes the statements and reasons for proving that corresponding angles are congruent:

step	statements	reasons
2	points $s$, $q$, $r$, and $t$ all lie on the same line.	given
3	$mangle sqt = 180^{circ}$	definition of a straight angle
4	$mangle sqv + mangle vqt = mangle sqt$	angle addition postulate
5		substitution property of equality
6	$mangle vqt + mangle zrs = 180^{circ}$	same - side interior angles theorem
7	$mangle sqv + mangle vqt = mangle vqt + mangle zrs$	substitution property of equality
8	$mangle sqv + mangle vqt - mangle vqt = mangle vqt + mangle zrs - mangle vqt$ <br> $mangle sqv = mangle zrs$	subtraction property of equality
	$angle sqv cong angle zrs$	definition of congruency

what is the missing statement for step 5? <br> $mangle sqv + mangle sqt$ <br> $mangle sqv + mangle vqt = 180^{circ}$ <br> $mangle sqv + mangle sqt = mangle vqt$

Explanation:

Step1: Identify prior valid statements

From Step3: $m\angle SQT = 180^\circ$
From Step4: $m\angle SQV + m\angle VQT = m\angle SQT$

Step2: Apply substitution property

Substitute $m\angle SQT = 180^\circ$ into Step4's equation.
$m\angle SQV + m\angle VQT = 180^\circ$

Answer:

$m\angle SQV + m\angle VQT = 180^\circ$