Question

in the diagram, the measure of angle 3 is 105°. which angle must also measure 105°?

Explanation:

Step1: Identify vertical angle of ∠3

Vertical angles are congruent. ∠1 is vertical to ∠3, so $m\angle1 = m\angle3 = 105^\circ$.

Step2: Identify corresponding angle of ∠3

Corresponding angles formed by a transversal cutting parallel lines are congruent. ∠7 is corresponding to ∠3, so $m\angle7 = m\angle3 = 105^\circ$.

Step3: Identify vertical angle of ∠7

Vertical angles are congruent. ∠5 is vertical to ∠7, so $m\angle5 = m\angle7 = 105^\circ$.

Answer:

Angle 1, Angle 5, and Angle 7 must also measure $105^\circ$.