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Answer:

m<1=117° by the Vertical Angles Congruence Theorem.

m<2=117° by the Alternate Exterior Angles Theorem.

Step-by-step explanation:

Vertical Angles Congruence Theorem- if two angles are vertical angles, then they are congruent.

Alternate Exterior Angles Theorem- when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.

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From the given diagram

m∠1 = 117° (Vertically opposite angles)

m∠2 = 117° (Corresponding angles)

In the diagram, we have two parallel lines and a transversal intersecting the two lines.

From one of the theorems, when two lines intersect, the opposite angles are equal. This is the vertically opposite angles theorem

In the diagram, angle 1 is opposite to the angle that measures 117°

∴ m∠1 = 117° (Vertically opposite angles)

  • Corresponding angles are found at different intersections but on the same side of each parallel line and the same side of the transversal line.

In the diagram, angle 1 and angle 2 are found at different intersections and on the same side of each of the parallel lines as well as on the same side of the transversal line. Therefore, they are corresponding angles.

From one of the theorems, corresponding angles are equal. That means angle 1 is equal to angle 2

Since, m∠1 = 117°

∴ m∠2 = 117° (Corresponding angles)

Hence, from the diagram

m∠1 = 117° (Vertically opposite angles)

m∠2 = 117° (Corresponding angles)

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