Question: Find the measure of \( \angle x \) given that \( p \parallel q \). \[ \begin{array}{c}…

Find the measure of \( \angle x \) given that \( p \parallel q \).

\[ \begin{array}{c} \text{Given:} \\ p \parallel q \\ \angle x = 132^\circ \\ \angle y = 28^\circ \\ \end{array} \]

Solution

To find the measure of angle \(a\) given that the lines \(p\) and \(q\) are parallel: Identify the relationship between angles. Since \(p \parallel q\), corresponding angles are equal. From the diagram, \(x = 152^\circ\) and \(y = 28^\circ\). Since \(x\) and \(v\) are corresponding angles, we have: \[ v = 152^\circ \] Since \(y\) and \(u\) are corresponding angles, we have: \[ u = 28^\circ \] Now, note that \(a\) and \(v\) are supplementary angles (they form a straight line): \[ a + v = 180^\circ \] Substitute the known value of \(v\): \[ a + 152^\circ = 180^\circ \] Solve for \(a\): \[ a = 180^\circ - 152^\circ \] \[ a = 28^\circ \] The measure of \(\angle a\) is \(28^\circ\).