Question

transversals of parallel lines angle relationships using the diagrams below, find the missing angle measures. be sure to name the angle relationships that help you justify your answers. in this diagram, lines q and r are parallel. in this diagram, lines a and b are parallel.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. In the first diagram, if one of the angles formed by the intersection of the transversal with the parallel lines is 49°.

Step2: Find m∠1

∠1 and the 49° - angle are vertical angles. So, $m\angle1 = 49^{\circ}$.

Step3: Find m∠2

∠2 and the 49° - angle are corresponding angles (since lines q and r are parallel). So, $m\angle2=49^{\circ}$.

Step4: Find m∠3

∠3 and ∠1 are supplementary (linear - pair). So, $m\angle3 = 180^{\circ}-49^{\circ}=131^{\circ}$.

Step5: Find m∠4

∠4 and ∠3 are vertical angles. So, $m\angle4 = 131^{\circ}$.

Step6: Find m∠5

∠5 and ∠2 are vertical angles. So, $m\angle5 = 49^{\circ}$.

Step7: Find m∠6

∠6 and ∠5 are supplementary (linear - pair). So, $m\angle6 = 180^{\circ}-49^{\circ}=131^{\circ}$.

Step8: Find m∠7

∠7 and ∠6 are vertical angles. So, $m\angle7 = 131^{\circ}$.

In the second diagram:

Step1: Identify vertical - angle relationship

If one angle is 125°, its vertical angle is also 125°.

Step2: Find m∠1

∠1 and the 125° - angle are vertical angles. So, $m\angle1 = 125^{\circ}$.

Step3: Find m∠2

∠2 and ∠1 are supplementary (linear - pair). So, $m\angle2 = 180^{\circ}-125^{\circ}=55^{\circ}$.

Step4: Find m∠3

∠3 and ∠2 are vertical angles. So, $m\angle3 = 55^{\circ}$.

Step5: Find m∠4

Since lines a and b are parallel, ∠4 and the 125° - angle are corresponding angles. So, $m\angle4 = 125^{\circ}$.

Step6: Find m∠5

∠5 and ∠4 are vertical angles. So, $m\angle5 = 125^{\circ}$.

Step7: Find m∠6

∠6 and ∠5 are supplementary (linear - pair). So, $m\angle6 = 180^{\circ}-125^{\circ}=55^{\circ}$.

Step8: Find m∠7

∠7 and ∠6 are vertical angles. So, $m\angle7 = 55^{\circ}$.

Answer:

First diagram:
$m\angle1 = 49^{\circ}$, $m\angle2 = 49^{\circ}$, $m\angle3 = 131^{\circ}$, $m\angle4 = 131^{\circ}$, $m\angle5 = 49^{\circ}$, $m\angle6 = 131^{\circ}$, $m\angle7 = 131^{\circ}$
Second diagram:
$m\angle1 = 125^{\circ}$, $m\angle2 = 55^{\circ}$, $m\angle3 = 55^{\circ}$, $m\angle4 = 125^{\circ}$, $m\angle5 = 125^{\circ}$, $m\angle6 = 55^{\circ}$, $m\angle7 = 55^{\circ}$