Answer:
m∠1 = 68°
m∠2 = 68°
m∠3 = 112°
m∠4 = 112°
m∠5 = 68°
m∠6 = 68°
m∠7 = 112°
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°