Question

in the figure below, ( l parallel m ). find the values of ( y ) and ( x ).
( y = 97 )
( x = square )

Explanation:

Step1: Use the property of supplementary angles

Since \(l\parallel m\), \(y + 83=180\) (same - side interior angles are supplementary). But we can also use the property of vertical angles and parallel lines. The angle \(y\) and \(83^{\circ}\) are supplementary (\(y = 180 - 83=97\)).

Step2: Use the property of vertical angles and parallel lines

The angle \((4x - 29)^{\circ}\) and \(83^{\circ}\) are congruent (corresponding angles as \(l\parallel m\)). So we set up the equation \(4x-29 = 83\).
Add \(29\) to both sides of the equation: \(4x=83 + 29\).
\(4x=112\).
Divide both sides by \(4\): \(x=\frac{112}{4}\).

Answer:

\(x = 28\)