Question

homework
find the measures
complete the table
measure
m∠1 = 103°
m∠2 = 77°
m∠3 = 77°
m∠4 = 103°
∠4 and same - side interior angles converse
angle whose measure is 20° and linear pair theorem
angle whose measure is 103° and alternate interior angles converse
∠2 and alternate exterior angles converse
angle whose measure is 20° and vertical angles theorem
∠1 and same - side interior angles converse
angle whose measure is 103° and alternate exterior angles converse
∠4 and corresponding angles converse

Explanation:

Step1: Recall angle - relationship theorems

Use properties of linear - pair, vertical angles, alternate interior/exterior angles, same - side interior angles, and corresponding angles.

Step2: Analyze linear - pair angles

If two angles form a linear pair, they are supplementary. If one angle is \(20^{\circ}\), its linear - pair angle is \(180^{\circ}-20^{\circ}=160^{\circ}\).

Step3: Analyze vertical angles

Vertical angles are equal. So if an angle is \(20^{\circ}\), its vertical angle is also \(20^{\circ}\).

Step4: Analyze alternate interior/exterior angles

Alternate interior angles and alternate exterior angles are equal when the lines are parallel. If an angle is \(103^{\circ}\), its alternate interior/exterior angle (when lines are parallel) is \(103^{\circ}\).

Step5: Analyze same - side interior angles

Same - side interior angles are supplementary when the lines are parallel. If one same - side interior angle is \(103^{\circ}\), the other is \(180^{\circ}-103^{\circ}=77^{\circ}\).

Step6: Analyze corresponding angles

Corresponding angles are equal when the lines are parallel.

Answer:

m\(\angle1 = 103^{\circ}\), m\(\angle2 = 77^{\circ}\), m\(\angle3 = 77^{\circ}\), m\(\angle4 = 103^{\circ}\)