1. Angle Relationships & Parallel Lines

2. Vocabulary The basics… Acute – Greater than 0°, but less than 90°
Right – Exactly 90°
Obtuse – Greater than 90°, but less than 180°
Straight – Exactly 180°
Reflex – Greater than 180°, but less than 360°
Full Turn – Exactly 360°

3. Vocabulary
The measure of the angle is the amount of opening between the sides of the angle.
Vertex – Point where rays meet.
Ray (side of angle)

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

5. These are examples of adjacent angles.
45º
80º
35º
55º
130º
50º
85º
20º

6. These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º

7. Transversal Transversal – A line that intersects two or more lines. n
Line n is a transversal.

8. Angles X and Angle Y are complementary and add up to 90 °.
Complementary Angles
Complementary Angles – Two angles that add up to 90°
Angles X and Angle Y are complementary and add up to 90 °. X Y

9. Complementary Angles but not Adjacent
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

10. Angles X and Angle Y are supplementary and add up to 180 °.
Supplementary Angles
Supplementary angles - Two angles that add up to 180°
Angles X and Angle Y are supplementary and add up to 180 °. X Y

11. Supplementary Angles Adjacent and Supplementary Angles
40º
140º
120º
60º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

12. Vertical Angles
Vertical Angles - A pair of opposite angles formed by the intersection of two lines. Vertical angles are always equal. A
Angle A and Angle B are vertical angles. They are equal! B

13. Vertical Angles A and C are vertical! B and D are vertical! B C A

14. Corresponding Angles
Corresponding angles – Two congruent angles that lie on the same side of the transversal.
A and B are corresponding angles. A B
Line n is a transversal. n

15. Alternate Interior Angles
A =  C
B =  D
They are alternate interior angles.
(Interior = Inside!) A B D C n
Line n is a transversal.

16. Alternate Exterior Angles
A =  C
B =  D
They are alternate exterior angles.
(Exterior = Outside!) A B D C n
Line n is a transversal.

17. Properties of Parallel Lines
Name the…
Corresponding Angles
Vertical Angles
Supplementary Angles
Alternate Interior Angles
Alternate Exterior Angles
A & E, B & F, C & G, D & H
A & D, B & C, F & G, E & H
A & B, B & D, D & C, etc…
C & F, D & E
A & H, B & G A B C D E F G H

18. Try this…
Find the missing angle. x°
36°
90 – 36 = 54°

19. Try this…
Solve for x.
3x°
2x°
3x + 2x = 90°
5x = 90
x = 18

20. Try this… Solve for x. 2x + 5 + x + 25 = 90° 3x + 30 = 90 3x = 60

21. Try this…
Solve for x. x
138°
180 – 138 = 42°

22. Try this…
Solve for x. 4x 5x
4x + 5x = 180
9x = 180
x = 20

23. Try this… Solve for x. 2x + 10 + 3x + 20 = 180 5x + 30 = 180 5x = 150

24. Try this… Find the missing angles. A = 138° D = 42° B = 138° E = 138°C D E G F
A = 138°
B = 138°
C = 42°
D = 42°
E = 138°
F = 138°
G = 42°

25. Try this… Find the missing angles. 70 + 70 + b = 180 40 + 65 + d = 180
70 °
70 ° b°
40 °
Hint: The 3 angles in a triangle sum to 180°.
d °
65 °
b = 180
140 + b = 180
b = 40°
d = 180
105 + d = 180
d = 75°