Question

given: two parallel lines intersected by a transversal. solve for x. find the value of the angles listed.

Explanation:

Step1: Identify angle - relationship

When two parallel lines are intersected by a transversal, the corresponding angles are equal. Here, \((56 - 5x)^{\circ}\) and \((62 - 8x)^{\circ}\) are corresponding angles, so \(56 - 5x=62 - 8x\).

Step2: Solve the equation for x

Add \(8x\) to both sides of the equation: \(56 - 5x+8x=62 - 8x+8x\), which simplifies to \(56 + 3x=62\). Then subtract 56 from both sides: \(3x=62 - 56\), so \(3x = 6\). Divide both sides by 3: \(x=\frac{6}{3}=2\).

Step3: Find the angle values

Substitute \(x = 2\) into \((56 - 5x)^{\circ}\): \(56-5\times2=56 - 10 = 46^{\circ}\). Substitute \(x = 2\) into \((62 - 8x)^{\circ}\): \(62-8\times2=62 - 16 = 46^{\circ}\).

Answer:

\(x = 2\), and the measure of both angles \((56 - 5x)^{\circ}\) and \((62 - 8x)^{\circ}\) is \(46^{\circ}\)