Download 1.5 Describe Angle Pair Relationships

Review - Midpoint and Distance
formula
A M B
B
(-9, 4) (-5, 4) (-1, 4)
D
(6, 7)
M • (4.5, 4)
C (3, 1)
C • (0,-5)
Questions on Homework 1.3??
Warm up
1. The sum of two numbers is 90 and one number is
4 times the other. Write an equation and solve to find
the numbers.
ANSWER
2. Find m
ANSWER
x + 4x = 90; 18, 72
ABD. What kind of angle is it?
180° , straight
Questions on 1.4?
1.5 Lesson
Describe Angle Pair
Relationships
Complementary Angles
2 angles that add to equal 90.
Examples:
Way to remember:
“It is right to give complements”
Supplementary Angles
2 angles are supplementary if the sum of
their angle measure is 180.
Example:
These two angles are supplementary.
Note that these two angles can be "pasted" together to form a straight
line!
Way to remember:
“S stand for straight”
Adjacent Angles
2 angles next to each other that share a
common vertex and side, but have no
common interior points.
A &B are adjacent
angles
GUIDED PRACTICE
1.
for Example 1
In the figure, name a pair of complementary
angles, a pair of supplementary angles, and a
pair of adjacent angles.
Because FGK and HGK
share a common vertex and
side, they are adjacent.
Because 41° + 49° = 90°, FGK
and GKL are complementary
angles.
Because 49° + 131° = 180°,
supplementary angles.
HGK and
GKL are
GUIDED PRACTICE
2.
for Example 1
Are KGH and LKG adjacent angles? Explain.
Nope!
While they do share a common. Adjacent angles
do not have common interior points.
EXAMPLE 2 Find measures of a complement and a supplement
a.
Given that
find m 2.
1 is a complement of
2 and m
SOLUTION
a.
You can draw a diagram with complementary
adjacent angles to illustrate the relationship.
m
2 = 90° – m 1 = 90° – 68° = 22
1 = 68°,
EXAMPLE 2 Find measures of a complement and a supplement
b.
Given that
find m 3.
3 is a supplement of
4 and m
4 = 56°,
SOLUTION
b.
You can draw a diagram with supplementary
adjacent angles to illustrate the relationship.
m
3 = 180° – m 4 = 180° –56° = 124°
EXAMPLE 3 Find angle measures
Sports
When viewed from the side, the frame of a ballreturn net forms a pair of supplementary angles with
the ground. Find m BCE and m ECD.
EXAMPLE 3 Find angle measures
SOLUTION
STEP 1
m
Use the fact that the sum of the measures
of supplementary angles is 180°.
BCE + m  ECD = 180° Write equation.
(4x+ 8)° + (x + 2)° = 180°
5x + 10 = 180
5x = 170
x = 34
Substitute.
Combine like terms.
Subtract 10 from each side.
Divide each side by 5.
EXAMPLE 3 Find angle measures
STEP 2
Evaluate: the original expressions when x = 34.
m
BCE = (4x + 8)° = (4 34 + 8)° = 144°
m
ANSWER
ECD = (x + 2)° = ( 34 + 2)° = 36°
The angle measures are 144° and 36°.
Angles Formed by the Intersection of 2
Lines
 Click Me!
Linear Pair
A linear pair is formed by two angles that are
adjacent (share a leg) and supplementary (add
up to 180°)
“forms a line”
Vertical Angles
A pair of non-adjacent angles formed by the
intersection of two straight lines
“When you draw over
the 2 angles it forms
an X”
EXAMPLE 4
Identify angle pairs
Identify all of the linear pairs and all of the
vertical angles in the figure at the right.
SOLUTION
To find linear pairs, look for adjacent angles whose
noncommon sides are opposite rays.
ANSWER
1 and 4 are a linear pair.
are also a linear pair.
4 and
To find vertical angles, look or
angles formed by intersecting lines.
ANSWER
1 and
5 are vertical angles.
5
Example 5
Two angles form a linear pair. The measure of
one angle is 5 times the measure of the other.
Find the measure of each angle.
Example 6
Given that m5 = 60 and m3 = 62, use
your knowledge of linear pairs and vertical
angles to find the missing angles.
Wrap Up
 sketches the angle pairs I describe.
 be sure to make up angles measures that
would fit the description.
 There are millions of answers that could be
correct.
 If it is not possible, write not possible.