Question

a diagonal walkway cuts through a park bordered by two parallel streets. the parks department plans by the dashed line segment in the figure below. what is the value of x?
(figure shows two parallel streets, a walkway, a 132° angle, and a dashed perpendicular segment with angle x°)
options: 42, 90, 48, 138

Explanation:

Step1: Identify supplementary angle

The 132° angle and its adjacent angle between the top street and the dashed line are supplementary.
$180^\circ - 132^\circ = 48^\circ$

Step2: Use right triangle angle sum

The dashed line is perpendicular to the bottom street, forming a right triangle. The sum of angles in a triangle is 180°.
$x = 180^\circ - 90^\circ - 48^\circ$

Step3: Calculate final value

Simplify the expression to find $x$.
$x = 42^\circ$

Answer:

42