Pre-AP Bellwork

6) Claire draws an angle that measures 56. Justin draws a congruent angle.

Justin says his angle is obtuse. Is he correct? Why or why not?

Pre-AP Bellwork

7) ∠MLN and ∠JLK are complementary, m∠MLN = 7x − 1, and

m∠JLK = 4x + 3.

a. Solve for x.

b. Find m∠MLN and m∠JKL.

c. Show how you can check your answer.

Pre-AP Bellwork

8)Describe all the situations in which the following statements aretrue.

a. Two vertical angles are also complementary.

b. A linear pair is also supplementary.c. Two supplementary angles are also a

linear pair.d. Two vertical angles are also a linear pair.

Pre-AP Bellwork

Find the measure of each angle in the angle pair described.9) The measure of one angle is 5 times the measure of its complement.

10) The measure of an angle is 30 less than twice its supplement.

1-5 Exploring Angle Pairs

Adjacent angles- two coplanar angles with a common side, a common vertex, and no common interior points

Which angles are adjacent?

1 32

4

1&2, 2&3, 3&4, 4&1

Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.

1&3, 2&4

Then what do we call 1&3?

Linear Pair (of angles)

2 adjacent angles whose non-common sides are opposite rays.

1 2

Example Vertical angles?

1 & 4

Adjacent angles?

1&2,2&3,

3&4,4&5,5&1

Linear pair?

5&4, 1&5

Adjacent angles not a linear pair?

1&2,2&3,3&4

1 3

2

5 4

Important Facts

Vertical Angles are congruent.

The sum of the measures of the angles in a linear pair is 180o.

Example:

If m5=130o, find

m3

m6

m4

5 3

4

6

=130o

=50o

=50o

Example:

Find x,y

mABE

mABD

mDBC

mEBC

3x+5o y+20ox+15o 4y-15o

x=40

y=35

mABE=125o

mABD=55o

mDBC=125o

mEBC=55o

A

B

C

D

E

Complementary Angles

2 angles whose sum is 90o

1

2

35o

A

55o

B1 & 2 are complementary

A & B are complementary

Supplementary Angles

2 angles whose sum is 180o

1

2

130o 50o

X Y

1 & 2 are supplementary.

X & Y are supplementary.

Ex: A & B are supplementary. mA is 5 times mB. Find mA & mB.

mA + mB = 180o

mA = 5(mB)

Now substitute!

5(mB) + mB = 180o

6(mB)=180o

mB=30o

mA=150o