Question

lines r and s are parallel. find the value of x, then find the measure of ∠1 and ∠2. m∠1=(76 - 2x)° m∠2=(92 - 3x)° x = □ (type an integer or a fraction.)

Explanation:

Step1: Use property of parallel lines

Since lines R and S are parallel, ∠1 and ∠2 are equal (corresponding - angles or alternate - interior angles, depending on the figure's context). So, we set up the equation \(76 - 2x=92 - 3x\).

Step2: Solve the equation for x

Add \(3x\) to both sides of the equation: \(76 - 2x+3x=92 - 3x+3x\), which simplifies to \(76 + x=92\). Then subtract 76 from both sides: \(x=92 - 76\).

Step3: Calculate the value of x

\(x = 16\).

Step4: Find the measure of ∠1

Substitute \(x = 16\) into the expression for \(m\angle1\): \(m\angle1=76-2\times16=76 - 32 = 44^{\circ}\).

Step5: Find the measure of ∠2

Substitute \(x = 16\) into the expression for \(m\angle2\): \(m\angle2=92-3\times16=92 - 48 = 44^{\circ}\).

Answer:

\(x = 16\), \(m\angle1 = 44^{\circ}\), \(m\angle2 = 44^{\circ}\)