Question

identify all the numbered angles that are congruent to the given angle. justify your answers. 7. 8. 9. 10. developing proof

Explanation:

Step1: Recall angle - congruence rules

Vertical angles are congruent and corresponding angles (when two parallel lines are cut by a transversal) are congruent.

Step2: Analyze problem 7

Angle 1 and angle 5 are corresponding angles, angle 2 and angle 6 are corresponding angles, angle 3 and angle 7 are corresponding angles. Also, vertical - angle pairs are: angle 1 and angle 2, angle 3 and angle 6, angle 4 and angle 5, angle 7 and angle 8. Given an angle of 65°, the congruent angles are: ∠1, ∠3, ∠5, ∠7 because ∠1 and ∠2 are vertical angles, ∠3 and ∠2 are supplementary (180 - 65=115), ∠5 and ∠2 are corresponding angles, ∠7 and ∠2 are vertical - angles of corresponding angles.

Step3: Analyze problem 8

For the given 51° angle, the congruent angles are the vertical - angle pairs and corresponding angles. The congruent angles are ∠1, ∠3, ∠5, ∠7. ∠1 and ∠2 are vertical angles, ∠3 and ∠2 are corresponding angles, ∠5 and ∠2 are vertical - angles of corresponding angles, ∠7 and ∠2 are corresponding angles of vertical - angles.

Step4: Analyze problem 9

For the 120° angle, the congruent angles are ∠1, ∠3, ∠5. ∠1 and ∠2 are vertical angles, ∠3 and ∠2 are corresponding angles, ∠5 and ∠2 are vertical - angles of corresponding angles.

Answer:

1. Congruent to the 65° angle: ∠1, ∠3, ∠5, ∠7
2. Congruent to the 51° angle: ∠1, ∠3, ∠5, ∠7
3. Congruent to the 120° angle: ∠1, ∠3, ∠5