Download Vertical Angles

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 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 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&  2,  2&  3,  3&  4,  4&
1
Then what do we call  1& 
3?
2
1
3
4
Vertical Angles – 2 angles
that share a common vertex &
whose sides form 2 pairs of
opposite rays.
 1&  3,  2&  4
Linear Pair (of angles)

2 adjacent angles whose non-common sides are
opposite rays.
Example

Vertical angles?
1&4

Adjacent angles?
2
 1&  2,  2&  3,
1
 3&  4, 4&  5,  5&  1
5

Linear pair?
 5&  4,  1&  5

Adjacent angles not a linear pair?
 1&  2, 2&  3,  3&  4
3
4
Important Facts

Vertical Angles are congruent.

The sum of the measures of the angles in a linear pair is 180o.
Example:

If m  5=130o, find
4
m  3 =130o
m  6 =50o
m  4 =50o
5
3
6
Example:
A
E

Find x,y
B
D
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

2 angles whose sum is 90o
35o
1
2
 1 &  2 are complementary
 A &  B are complementary
55o
A
B
Supplementary Angles

2 angles whose sum is 180o
 1 &  2 are
supplementary.
 X &  Y are
supplementary.
130o
X
50o
Y
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