Two angles are adjacent if they share a

Two angles are adjacent if they share a common vertex and side, but have no common interior points. SIDE BY SIDE…shoulder to shoulder. NO YES

Two adjacent angles are a linear pair if their noncommon sides are opposite rays. They form a straight line… SIDE BY SIDE…shoulder to shoulder. 1 2 The sum of the measure s of angles that form a linear pair is 180º

Please Identify in your notes all LINEAR PAIRS i m k e j h f g

SOME POSSIBLE ANSWERS i m k e j h f g

MORE POSSIBLE ANSWERS i m k e j h f g

1. Determine whether each statement is true or false. 1 2

2. 4 5

3. 6 3

4. C 8 7 A T

5. C 8 7 A T

Two angles are vertical angles if their sides form two pairs of opposite rays Vertical angles are always congruent. Angles 1 and 2 are vertical angles Angles 3 and 4 are also vertical angles 1 3 4 2

Identify all pairs of VERTICAL ANGLES i m k e j h f g a b d c

What is the measure of the angle? 5 y -50 What type of angles are these? 4 y-10 5 y - 50 = 4 y - 10 y = 40 Plug y back into our angle equations and we get

Identify each pair of angles as adjacent, vertical, and/or as a linear pair. Example 1: 2 1 ADJACENT 3 4 5

Identify each pair of angles as adjacent, vertical, and/or as a linear pair. Example 2: 2 VERTICAL 1 3 4 5

Identify each pair of angles as adjacent, vertical, and/or as a linear pair. Example 3: 2 1 ADJACENT 3 4 5

Identify each pair of angles as adjacent, vertical, and/or as a linear pair. Example 4: 2 1 ADJACENT, LINEAR PAIR 3 4 5

Find x, y, and z. Example 5: 129, 51, 129

L Example 6: Find x. T P A O X=8

L Example 7: T P Find Since we have already found the value of x, all we need to do now is to plug it in for LAT. 155 A O

Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other. 1 These are supplements of each other because their angles add up to 180. 2

Example 1 Find the value of x.

Example 2 Find the value of x.

Example 3 Find the value of x.

Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 These are complements of each other because their angles add up to be 90. 2

How can I remember the difference between complementary and supplementary? Hmmm…. . It’s just nice to give people compliments. Remember the sentence below and it will help remind you that complementary angles are just the ones that add up to a right angle. A compliment is just right.

Example 4 Find the value of x.

Example 5 Find the value of x.

1 5 2 4 3 Are angles 1 and 2 a linear pair? no Are angles 1 and 3 adjacent angles? no Are angles 3 and 4 a linear pair? yes Are angles 2 and 3 adjacent angles? yes

1 5 2 4 3 Are angles 4 and 5 supplementary angles? no Are angles 2 and 3 complementary angles? no Are angles 4 and 3 supplementary angles? yes Are angles 2 and 1 complementary angles? yes