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Answer:

m∠1 = 68°

m∠2 = 68°

m∠3 = 112°

m∠4 = 112°

m∠5 = 68°

m∠6 = 68°

m∠7 = 112°

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

Angles on a Straight Line

Angles on a straight line sum to 180°.

Applying the Vertical Angle Theorem and the Corresponding Angles Postulate:

⇒ m∠3 = m∠4 = m∠7 = 112°

To find the measure of angle 2, apply the Angles on a Straight Line theorem:

⇒ m∠2 = 180° - 112° = 68°

Applying the Vertical Angle Theorem and the Corresponding Angles Postulate:

⇒ m∠2 = m∠1 = m∠5 = m∠6 = 68°

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