Question

use what you know about parallel lines and transversals to label each of the missing angle measures in the picture below
*notice that when parallel lines are crossed by a transversal, any pair of the angles formed will either be _ or _
practice finding missing angles below. be sure to justify your answers using specific vocabulary.
questions 1&2
line r is parallel to line s. the ( mangle2 = 55^circ ).

1. find the measure of ( angle3 ). how do you know?
2. find the measure of ( angle7 ). how do you know?

questions 3&4
line j is parallel to line k. the ( mangle5 = 102^circ ).

1. find the measure of ( angle4 ). how do you know?
2. find the measure of ( angle1 ). how do you know?

question 5

1. use the picture from questions 3 - 4 to mark the following statements as true or false. correct any false statements in the space on the right.

___ ( angle2 ) and ( angle8 ) are corresponding angles.
___ ( angle3 ) and ( angle5 ) are congruent angles.
___ ( angle1 ) and ( angle8 ) are alternate interior angles.
___ ( angle5 ) and ( angle8 ) are vertical angles.
___ ( angle1 ) and ( angle7 ) are supplementary angles.

Explanation:

Step1: Solve for ∠3

$\angle 3 = \angle 2 = 55^\circ$ (Vertical Angles Congruence)

Step2: Solve for ∠7

$\angle 7 = \angle 2 = 55^\circ$ (Alternate Exterior Angles Congruence)

Step3: Solve for ∠4

$\angle 4 = \angle 5 = 102^\circ$ (Alternate Interior Angles Congruence)

Step4: Solve for ∠1

$\angle 1 = 180^\circ - \angle 5 = 180^\circ - 102^\circ = 78^\circ$ (Supplementary Linear Pair)

Step5: Evaluate Question 5 statements

1. $\angle 2$ and $\angle 8$: Corresponding angles (True)
2. $\angle 3$ and $\angle 5$: Alternate interior angles (Congruent, True)
3. $\angle 1$ and $\angle 8$: Not alternate interior (False; they are corresponding angles)
4. $\angle 5$ and $\angle 8$: Linear pair (Not vertical, False; they are supplementary)
5. $\angle 1$ and $\angle 7$: Corresponding angles (Congruent, not supplementary; False)

Answer:

1. $m\angle 3 = 55^\circ$; Vertical angles are congruent.
2. $m\angle 7 = 55^\circ$; Alternate exterior angles are congruent.
3. $m\angle 4 = 102^\circ$; Alternate interior angles are congruent.
4. $m\angle 1 = 78^\circ$; Linear pair angles are supplementary.

5.

• True
• True
• False; $\angle 1$ and $\angle 8$ are corresponding angles.
• False; $\angle 5$ and $\angle 8$ are supplementary linear pair angles.
• False; $\angle 1$ and $\angle 7$ are congruent corresponding angles.