Question

given that the two parallel lines are cut by a transversal, and the measure of angle 2 is 65 degrees. find each of the missing angles.

m∠1 = 115 degrees
m∠3 = 115 degrees
m∠4 = 65 degrees
m∠7 = 65 degrees

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. Since the sum of angles in a linear - pair is 180 degrees and $m\angle2 = 65$ degrees, then $m\angle1=180 - 65=115$ degrees.

Step2: Use vertical - angle property

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are equal, so $m\angle3 = m\angle1 = 115$ degrees.

Step3: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal, so $m\angle4 = m\angle2 = 65$ degrees.

Step4: Use corresponding - angle property

$\angle4$ and $\angle7$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So $m\angle7 = m\angle4 = 65$ degrees.

Answer:

$m\angle1 = 115$ degrees, $m\angle3 = 115$ degrees, $m\angle4 = 65$ degrees, $m\angle7 = 65$ degrees