Question

special angle pair measures-notes
ccss.math.content.hsg.co.c.9
when two parallel lines are cut by a transversal, they create _ angles. these angles form a pattern of _ angles and _ angles.
examples: find all missing angles.
1.
2.
3.
4.
5.
6.

Explanation:

Step1: Recall angle - pair properties

When two parallel lines are cut by a transversal, they create special - angle pairs. The pattern consists of corresponding angles (equal in measure), alternate - interior angles (equal in measure), alternate - exterior angles (equal in measure), and same - side interior angles (supplementary, sum to 180°).

Step2: Solve for Example 1

The given angle is 71°. The angle opposite to it (vertical angle) is also 71°. The angle adjacent to 71° on the same straight - line is 180 - 71=109°. The corresponding, alternate - interior, and alternate - exterior angles to 71° are 71°, and the corresponding, alternate - interior, and alternate - exterior angles to 109° are 109°.

Step3: Solve for Example 2

The given angle is 35°. The vertical angle to 35° is 35°. The angle adjacent to 35° on the same straight - line is 180 - 35 = 145°. The corresponding, alternate - interior, and alternate - exterior angles to 35° are 35°, and the corresponding, alternate - interior, and alternate - exterior angles to 145° are 145°.

Step4: Solve for Example 3

The given angle is 42°. The vertical angle to 42° is 42°. The angle adjacent to 42° on the same straight - line is 180 - 42=138°. The corresponding, alternate - interior, and alternate - exterior angles to 42° are 42°, and the corresponding, alternate - interior, and alternate - exterior angles to 138° are 138°.

Step5: Solve for Example 4

The given angle is 117°. The vertical angle to 117° is 117°. The angle adjacent to 117° on the same straight - line is 180 - 117 = 63°. The corresponding, alternate - interior, and alternate - exterior angles to 117° are 117°, and the corresponding, alternate - interior, and alternate - exterior angles to 63° are 63°.

Step6: Solve for Example 5

Since the lines are perpendicular, all angles are 90°. Vertical angles are 90° and angles on the same straight - line are supplementary (180 - 90=90°).

Step7: Solve for Example 6

The given angle is 158°. The vertical angle to 158° is 158°. The angle adjacent to 158° on the same straight - line is 180 - 158 = 22°. The corresponding, alternate - interior, and alternate - exterior angles to 22° are 22°, and the corresponding, alternate - interior, and alternate - exterior angles to 158° are 158°.

Answer:

For Example 1: The missing angles are 71°, 109°, 71°, 109°.
For Example 2: The missing angles are 35°, 145°, 35°, 145°.
For Example 3: The missing angles are 42°, 138°, 42°, 138°.
For Example 4: The missing angles are 117°, 63°, 117°, 63°.
For Example 5: All angles are 90°.
For Example 6: The missing angles are 22°, 158°, 22°, 158°.