Question

in the figure below, m || k. find the values of y and z.

Explanation:

Step1: Use the property of alternate - interior angles

Since \(m\parallel k\), the angle of \(65^{\circ}\) and \(y\) are alternate - interior angles. So \(y = 65^{\circ}\) (alternate - interior angles are equal when two parallel lines are cut by a transversal).

Step2: Use the property of vertical angles

The angle \(y\) and \((6z - 83)^{\circ}\) are vertical angles. So \(y=6z - 83\).
Substitute \(y = 65\) into the equation \(65=6z - 83\).
Add \(83\) to both sides of the equation: \(65 + 83=6z\), i.e., \(148 = 6z\).
Divide both sides by \(6\): \(z=\frac{148}{6}=\frac{74}{3}\approx24.67\).

Answer:

\(y = 65\), \(z=\frac{74}{3}\)