Question

in the figure below, m || n and p || q. find the values of y and z.
62°
y°
(3z - 31)
y =
z =

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\) and \(p\parallel q\), the angle of \(62^{\circ}\) and the angle \(y^{\circ}\) are corresponding angles. Corresponding angles formed by two pairs of parallel - lines are equal. So \(y = 62\).

Step2: Use the property of alternate - interior angles

The angle \(y^{\circ}=62^{\circ}\) and the angle \((3z - 31)^{\circ}\) are alternate - interior angles. Alternate - interior angles formed by two pairs of parallel - lines are equal. So we set up the equation \(3z-31 = 62\).
Add 31 to both sides of the equation: \(3z=62 + 31\), so \(3z=93\).
Divide both sides by 3: \(z=\frac{93}{3}=31\).

Answer:

\(y = 62\)
\(z = 31\)