Question

part of a city map is shown. if (mangle5 = x^{circ}), which angles also have a measure of (x^{circ})? select all that apply. a. (angle1) b. (angle4) c. (angle9) d. (angle12)

Explanation:

Step1: Identify angle - relationships

Parallel lines are shown on the city - map grid. When two parallel lines are cut by a transversal, corresponding angles are congruent, alternate interior angles are congruent, and vertical angles are congruent.

Step2: Analyze angle 5

Angle 5 and angle 1 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles have the same measure. So \(m\angle1 = m\angle5=x^{\circ}\).

Step3: Analyze other angles

Angle 5 and angle 9 are vertical angles. Vertical angles are always congruent, so \(m\angle9 = m\angle5=x^{\circ}\).
Angle 5 and angle 4 are neither corresponding, alternate interior, nor vertical angles, so \(m\angle4
eq m\angle5\). Angle 5 and angle 12 are neither corresponding, alternate interior, nor vertical angles, so \(m\angle12
eq m\angle5\).

Answer:

A. \(\angle1\), C. \(\angle9\)