Angle Relationships & Parallel Lines Pre-Algebra

Adjacent angles are “side by side” and share a common ray. 45º 15º

These are examples of adjacent angles. 55º 35º 50º130º 80º 45º 85º 20º

These angles are NOT adjacent. 45º55º 50º 100º 35º

Complementary Angles sum to 90° 40° 50°

Complementary angles add up to 90º. 60º 30º 40º 50º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Supplementary Angles sum to 180° 30° 150°

Supplementary angles add up to 180º. 60º120º 40º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Vertical Angles are opposite one another. Vertical angles are congruent. 100°

Vertical Angles are opposite one another. Vertical angles are congruent. 80°

Lines l and m are parallel. l || m 120° l m Note the 4 angles that measure 120°. n Line n is a transversal.

Lines l and m are parallel. l || m 60° l m Note the 4 angles that measure 60°. n Line n is a transversal.

Lines l and m are parallel. l || m 60° l m There are many pairs of angles that are supplementary. There are 4 pairs of angles that are vertical. 120° n Line n is a transversal.

If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

Practice Time!

1) Find the missing angle. 36° ?°?°

1) Find the missing angle. 36° ?°?° 90 ° – 36 = 54°

2) Find the missing angle. 64° ?°?°

2) Find the missing angle. 64° ?°?° 90 ° – 64° = 26°

3) Solve for x. 3x° 2x°

3) Solve for x. 3x° 2x° 3x° + 2x° = 90° 5x = 90 x =18

4) Solve for x. 2x + 5 x + 25

4) Solve for x. 2x + 5 x + 25 (2x + 5) + (x + 25) = 90 3x + 30 = 90 3x = 60 x = 20

5) Find the missing angle. ?°?° 168°

5) Find the missing angle. ?°?° 168° 180° – 168° = 12°

6) Find the missing angle. 58° ?°?°

6) Find the missing angle. 58° ?°?° 180° – 58° = 122°

7) Solve for x. 4x 5x

7) Solve for x. 4x 5x 4x + 5x = 180 9x = 180 x = 20

8) Solve for x. 2x x + 20

8) Solve for x. 2x x + 20 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30

9) Lines l and m are parallel. l || m Find the missing angles. 42° l m b°b° d°d° f°f° a ° c°c° e°e° g°g°

9) Lines l and m are parallel. l || m Find the missing angles. 42° l m 138°

10) Lines l and m are parallel. l || m Find the missing angles. 81° l m b°b° d°d° f°f° a ° c°c° e°e° g°g°

10) Lines l and m are parallel. l || m Find the missing angles. 81° l m 99°

11) Find the missing angles. 70 ° b° 70 ° d °65 ° Hint: The 3 angles in a triangle sum to 180°.

11) Find the missing angles. 70 ° 40° 70 ° 75 °65 ° Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles. 45 ° b° 50 ° d °75 ° Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles. 45 ° 85° 50 ° 20°75 ° Hint: The 3 angles in a triangle sum to 180°.

In the figure a || b. 13. Name the angles congruent to  Name all the angles supplementary to  If m  1 = 105° what is m  3? 16. If m  5 = 120° what is m  2?  1,  5,  7  1,  3,  5,  7 105° 60°

The End