Question

find the measures of
angle whose measure is 62° and alternate interior angles converse
angle whose measure is 62° and alternate exterior angles converse
∠2 and linear - pair theorem
angle whose measure is 62° and vertical angles theorem
angle whose measure is 62° and linear - pair theorem
angle whose measure is 62° and corresponding angles converse
measure
m∠1=
m∠2=
m∠3=
m∠4=

Explanation:

Step1: Recall vertical - angles property

Vertical angles are equal. If one angle is 62°, its vertical - angle has the same measure.

Step2: Recall linear - pair property

A linear pair of angles is supplementary (sum to 180°). If one angle of a linear pair is 62°, the other is 180° - 62°=118°.

Step3: Recall corresponding, alternate - interior and alternate - exterior angles properties

Corresponding angles, alternate - interior angles and alternate - exterior angles formed by parallel lines and a transversal are equal.

Let's assume the given 62° angle and ∠1 are vertical angles, so m∠1 = 62°.
If ∠1 and ∠2 form a linear pair, then m∠2=180 - 62=118°.
If ∠2 and ∠3 are vertical angles, then m∠3 = 118°.
If ∠3 and ∠4 form a linear pair, then m∠4 = 62°.

Answer:

m∠1 = 62°
m∠2 = 118°
m∠3 = 118°
m∠4 = 62°