Question

find the value of x. then find the measure of each labeled angle.

Explanation:

Step1: Use angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is 360°. One angle is 90°, and the other two angles are \(x^{\circ}\) and \((x - 48)^{\circ}\). So, \(90+x+(x - 48)+y=360\). Since the fourth - angle is not given and we assume it is not relevant to the parallel - side relationship (the arrows suggest parallel sides), we can also use the fact that \(x+(x - 48)=180\) (co - interior angles between parallel lines are supplementary).
\[x+(x - 48)=180\]

Step2: Simplify the equation

Combine like terms: \(x+x-48 = 180\), which gives \(2x-48=180\).
Add 48 to both sides of the equation: \(2x=180 + 48\), so \(2x=228\).
Divide both sides by 2: \(x=\frac{228}{2}=114\).

Step3: Find the measure of \((x - 48)^{\circ}\)

Substitute \(x = 114\) into \((x - 48)^{\circ}\). Then \(x-48=114 - 48=66\).

Answer:

\(x = 114\)
\((x - 48)=66\)