Chapter 1 1 4 Pair of Angles Warmup

Chapter 1 1 -4 Pair of Angles

Warm-up 1. BD bisects ABC, m ABD = , and m DBC = (y + 4)°. Find m ABC. 2. m WYZ = (2 x – 5)° and m XYW = (3 x + 10)°. Find the value of x.

Warm-up answers � 1. BD bisects ABC, m ABD = m DBC = (y + 4)°. Find m ABC. , and �Answer: 32° � 2. m WYZ = (2 x – 5)° and m XYW = (3 x + 10)°. Find the value of x. �Answer: 35

Objectives �Students will be able to: �* Identify adjacent, vertical, complementary, and supplementary angles. �* Find measures of pairs of angles.

1 -4 pair of angles �What is an angle? �Answer: an angle is a figure formed by two rays with a common endpoint of vertex. �What are some of the different types of angles you have heard?

1 -4 pair of Angles �So today we are going to see different kinds of pair angles like �Linear pairs add up to 180

1 -4 pair of angles

1 -4 Pair of angles �You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. �You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

1 -4 Pair of Angles �Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical angles are two nonadjacent angles formed by two intersecting lines. 1 and 3 are vertical angles, as are 2 and 4. �Vertical angles are congruent.

1 -4 pair of Angles �Example #1 �Tell whether the following pair of angles are linear, adjacent , vertical or complementary. �From the Angle Pair relationship worksheet �Problem s 1, 2, 5 and 8 �Student Guide 3, 4, 6, 7

1 -4 Pair of Angles �Example #2 �From the angle pair worksheet problems 9, 10, 12 �Student guide 13, 14 and 18

1 -4 pair of angles �Example #3 �Angle pair worksheet Problem 19, 20 Student guide 21 and 22

1 -4 Pair of angles �Just Remember complementary add up to 90 and supplementary add up to 180. �Example #4 �Two angles are complementary. One angle is 4 times the other. The other angles is x+6. Find the two angles. �Answer: �Angle 1+angle 2=90 �(x+6)+4(x+6)=90 �X+6+4 x+24=90 � 5 x+30=90 � 5 x=60 �X=12 �Angle 1=18, Angle 2=72

1 -4 pair of angles �Example #5 �One angle is 5 x+3 and its supplementary angle is 3 times the other angle. Find x �Answer: � 5 x+3+3(5 x+3)=180 simplify � 5 x+3+15 x+9=180 combine like terms � 20 x+12=180 solve for x � 20 x=168 divide by 20 � X=8. 4

1 -4 pair of angles �Homework page 32 �Problems # 14, 18, 19 , 26, 29 �Finish the angle pair worksheet

Closure �Today we learned about the different pair angles like linear angles, adjacent angles, vertical angles. We also learned about complementary and supplementary angles. Tomorrow we are going to have a quiz and continue with 1 -5 part 1.