Question

lines r and s are parallel. find the value of x, then find the measure of ∠1 and ∠2
m∠1=(79−2x)°
m∠2=(92−3x)°
m∠1=53°
(type an integer or a fraction.)
m∠2=□°
(type an integer or a fraction.)
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Explanation:

Step1: Find the value of \(x\)

Given \(m\angle1=(79 - 2x)^{\circ}\) and \(m\angle1 = 53^{\circ}\), we set up the equation \(79-2x=53\).
Subtract \(79\) from both sides: \(-2x=53 - 79\), so \(-2x=-26\).
Divide both sides by \(-2\): \(x = 13\).

Step2: Calculate \(m\angle2\)

Substitute \(x = 13\) into \(m\angle2=(92-3x)^{\circ}\).
\(m\angle2=92-3\times13\).
First, calculate \(3\times13 = 39\).
Then, \(m\angle2=92 - 39=53^{\circ}\).

Answer:

\(m\angle2 = 53^{\circ}\)