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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.

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Pre ap bellwork
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 bellwork1
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 bellwork2
Pre-AP Bellwork

8)Describe all the situations in which the following statements are

true.

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 bellwork3
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.



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


Which angles are adjacent
Which angles are adjacent?

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

Then what do we call  1&  3?

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

 1&  3,  2&  4

2

1 3

4


Linear pair of angles
Linear Pair (of angles)

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

1 2


Example
Example

2

  • 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

5 4


Important facts
Important Facts

  • Vertical Angles are congruent.

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


Example1
Example:

  • If m  5=130o, find

    m  3

    m  6

    m  4

4

=130o

=50o

=50o

5 3

6


Example2

A

Example:

E

3x+5o y+20o

B

x+15o 4y-15o

D

  • Find x,y

    m  ABE

    m  ABD

    m  DBC

    m  EBC

C

x=40

y=35

mABE=125o

m  ABD=55o

m  DBC=125o

m  EBC=55o


Complementary angles
Complementary Angles

  • 2 angles whose sum is 90o

35o

1

2

55o

A

 1 &  2 are complementary

 A &  B are complementary

B


Supplementary angles
Supplementary Angles

  • 2 angles whose sum is 180o

 1 &  2 are supplementary.

 X &  Y are supplementary.

1 2

130o 50o

X Y


Ex a b are supplementary m a is 5 times m b find m a m b
Ex:  A &  B are supplementary. m  A is 5 times m  B. Find m  A & m  B.

m  A + m  B = 180o

m  A = 5(m  B)

Now substitute!

5(m  B) + m  B = 180o

6(m  B)=180o

m  B=30o

m  A=150o


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