1. C A D B mÐABC = 14x + 2, mÐCBD = 6x + 1, mÐABD = 25x – 27
Find x, mÐABC, mÐCBD, and mÐABD
WARMUP - A C D
mÐABC = 14x + 2 B
mÐABC = 14(6) + 2 = 86
mÐABC + mÐCBD = mÐABD
mÐCBD = 6x + 1
14x x + 1 = 25x – 27
mÐCBD = 6(6) + 1 = 37
20x + 3 = 25x – 27
3 = 5x – 27
mÐABD = 25x - 27
30 = 5x
mÐABD = 25(6) - 27 = 113
6 = x
x = 6 mÐABC = 86° mÐCBD = 37 ° mÐABD = 113 °

2. What are some special angle relationships?
Agenda:
Warmup
Review angles from yesterday
Special angle pairs

3. Complementary Angles
Definition: two angles whose measures have the sum of 90°.
35°
55°
20°
70°
Complementary Angles may or may not be
Adjacent Angles.

4. Supplementary Angles
Definition: two angles whose measures have the sum of 180°.
110°
70°
125°
55°
Supplementary Angles may or may not be
Adjacent Angles.

5. Definition: two supplementary, adjacent angles.
Linear Pair
Definition: two supplementary, adjacent angles.
120°
60°
Linear Pair = A Pair of Angles that forms a Line.

6. Definition: two non-adjacent angles formed by intersecting lines.
Vertical Angles
Definition: two non-adjacent angles formed by intersecting lines. 1 2 3 4
Ð1 and Ð2 are vertical angles.
Ð3 and Ð4 are vertical angles.

7. 1 4 3 2 Ð3@Ð4 Ð1@Ð2 What do you notice?
Theorem: Vertical Angles are Congruent.

8. 10x - 18 8x + 6 102 Find x. Applying new concepts with Algebra… C A Q
We know vertical angles are congruent; therefore the measure of vertical angles are equal and we can set these two expressions equal to one another.
10x – 18 = 8x + 6
2x = 24 x = 12

9. 18° x + 4x = 90° 5x = 90° 72° x = 18 What relationship do we see here?
Complementary Angles
18°
72°
x + 4x = 90° x°
4x°
5x = 90°
x = 18

10. Supplementary Angles
109°
71°
4x+3
6x+7
4x+3 + 6x+7 = 180°
x = 17
10x + 10 = 180
10x = 170

11. CHECK FOR UNDERSTANDING
P. 71 #15, 16, 20, 21
P. 72 #37
P. 79 #28, 29
P 80 #54, 55