1. Pa i r s o f A n g l e s 1. Adjacent Angles Two angles that share a common side and a common vertex, but do not overlap. 1. they have a common side: (line segment CB) 2. they have a common vertex:(point B) In the figure shown, a and b are adjacent angles. They have a common vertex a common side Angle ABC is adjacent to angle CBD (.O) (Ray OA.)

2. They are NOT Adjacent Angles angle PSQ and angle PSR overlap they only share a side, not a vertex they only share a vertex, not a side They Adjacent Angles they share a vertex and a side Which of the following are adjacent angles? Why?

3. and are adjacent angles. Find, if and. Solved Examples on Adjacent Angles Choices: A. 90 B. 26 C. 80 D. 16 Step1: Correct Answer : B Solution: Step 2: = 58 - 32 = 26 A D B C

4. Exercises: Given: <DOC = 45; <BOA= 35; <COB = 42 Find: 1.m<DOB m<COA m<DOA m<DOC + m<BOA m<DOB – m<BOA D B C A O 1.m<DOB = 87 2.m<COA =77 3.m<DOA = 122 4.m<DOC + m<BOA = 80 5.m<DOB – m<BOA = 52 Answers:

5. 2. Complementary angles Two angles are complementary if their sum is 90°. These two angles (40° and 50°) are Complementary Angles, because they add up to 90°. Notice that together they make a right angle. These two are complementary because 27° + 63° = 90° These two angles are complementary.

6. Sample Problems for Complementary Angles 1. If one angle is 60 degree find the measure of the other angle if the two angles are complementary to each other. Sol :- Since the two angles are complementary angles they must add up to 90 degree. So, Angle 1 + Angle 2 = 90 degree 60 + angle 2 = 90 degree. Angle 2 = 90 – 60 Angle 2 = 30 degrees 2. If one angle is 39 degree find the measure of angle 2 if the two angles are complementary to each other. Solution: 90 – 39 = 51 Angle 2 = 51 degrees. 3. Angle 1 measures 25 degrees and angle 2 measures 65 degrees. Are the angles complementary to each other? Ans : Yes, They are complementary to each other

7. 4. Find the complement angle of 40 degrees? Solution: 40 + x = 90 x = 90 – 40 x = 50. The complementary angle is 50. 5. Find the measures of the complementary angle of the following: a. 22 degrees b. 63 degrees c. 45 degrees d. 75 degrees 1) 90-22=68 2) 90-3o=27 3) 90-45=45 4) 90-75=15 Solution:

8. 5. Two complementary angles are A (x + 4)0 and B(2x – 7)0. Find the value of x and the measure of each angle. 2. Two complementary angles are the ratio 2 : 3, find these angles ASSIGNMENT: 3. The two complementary angles are (4x + 8)° and (4x + 10)°. Find the value of x from the given data. 4. (10 – 3x)˚ and (90 – 2x)˚ are complimentary angles. Solve for x. 1. Find whether the angles 72 degree and 18 degree are complementary angles.

9. 3. Linear pair Two angles are a linear pair if they have a common side and their If angle 1 and angle 2 are a linear pair, then angle1+ angle 2 = 180°. other sides are opposite rays.

10. 2. Supplementary angles Two angles are supplementary if their sum is 180°.

11. A linear pair is a pair of adjacent angles formed when two lines intersect. angles 1 and 3. Angles 1 and 2 angles 2 and 4, angles 3 and 4, Linear pairs are: 3. Linear pair Two angles are a linear pair if they have a common side and their

12. 4. Vertical angles Two angles are vertical angles iff the sides of one angle are opposite rays to the sides of the other. Vertical angles are the "opposite angles" that are formed by two intersecting lines. Note: If Angle 1 and angle 2 are vertical angles, then measure of angle 1 is equal to the measure of angle 2.