Question

in the figure below, (lparallel j). find the values of (x) and (y).

Explanation:

Step1: Use corresponding - angles property

Since \(l\parallel j\), the angle of \(74^{\circ}\) and the angle of \(x^{\circ}\) are corresponding angles. So \(x = 74\).

Step2: Use linear - pair or vertical - angles and angle - sum property

The angle of \(x^{\circ}=74^{\circ}\) and the angle of \((4y - 10)^{\circ}\) are vertical angles (or we can use the fact that they are equal because of parallel lines and angle - relationships). So we set up the equation \(4y-10=x\). Substitute \(x = 74\) into the equation: \(4y-10 = 74\).
Add 10 to both sides of the equation: \(4y=74 + 10=84\).
Divide both sides by 4: \(y=\frac{84}{4}=21\).

Answer:

\(x = 74\), \(y = 21\)