1. The document provides examples and explanations of different types of angle relationships including: complementary angles, supplementary angles, adjacent angles, linear pairs, and vertical angles. Examples are worked through step-by-step to find the measures of unknown angles using properties of these relationships. 2. Guided practice problems similar to the examples are provided for students to work through. The correct answers are given. 3. Key concepts covered include writing equations to represent angle relationships and solving them algebraically to find unknown angle measures. Diagrams are also used to illustrate and identify different angle pairs.

1. 1.51.5 Describe Angle Pair Relationships
Bell Thinger
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 x + 4x = 90; 18, 72
2. Find m ABD. What kind of angle is it?
ANSWER 180° , straight

2. 1.5

3. 1.5Example 1
SOLUTION
In the figure, name a pair of
complementary angles, a pair
of supplementary angles, and
a pair of adjacent angles.
Because 122° + 58° = 180°, CAD and RST are
supplementary angles.
Because BAC and CAD share a common vertex
and side, they are adjacent.
Because 32°
+ 58°
= 90°
, BAC and RST are
complementary angles.

4. 1.5Guided Practice
In the figure, name a pair of complementary
angles, a pair of supplementary angles, and a
pair of adjacent angles.
1.
FGK and GKL,
HGK and GKL,
FGK and HGK
ANSWER

5. 1.5Guided Practice
Are KGH and LKG adjacent angles ? Are
FGK and FGH adjacent angles? Explain.
2.
No, they do not share a common vertex.
No, they have common interior points.
ANSWER

6. 1.5Example 2
SOLUTION
a. Given that 1 is a complement of 2 and m 1 = 68°,
find m 2.
a. You can draw a diagram with complementary
adjacent angles to illustrate the relationship.
m 2 = 90° – m 1 = 90° – 68° = 22°

7. 1.5Example 3
b. You can draw a diagram with supplementary
adjacent angles to illustrate the relationship.
m 3 = 180° – m 4 = 180° –56° = 124°
SOLUTION
b. Given that 3 is a supplement of 4 and m 4 = 56°,
find m 3.

8. 1.5

9. 1.5Example 4
Sports
When viewed from the side, the frame of a ball-
return net forms a pair of supplementary angles with
the ground. Find m BCE and m ECD.

10. 1.5Example 4
SOLUTION
STEP 1 Use the fact that the sum of the measures
of supplementary angles is 180°.
Write equation.
(4x + 8)° + (x + 2)° = 180° Substitute.
5x + 10 = 180 Combine like terms.
5x = 170
x = 34
Subtract 10 from each side.
Divide each side by 5.
m BCE + m ECD = 180°
STEP 2 Evaluate: the original expressions when x = 34.
m ECD = (x + 2)° = ( 34 + 2)° = 36°
The angle measures are 144° and 36°.ANSWER
m BCE = (4x + 8)° = (4 34 + 8)° = 144°

11. 1.5 Guided Practice
3. Given that 1 is a complement of 2 and m 2 = 8o
,
find m 1.
82o
ANSWER
4. Given that 3 is a supplement of 4 and
m 3 = 117o
, find m 4.
63o
ANSWER
5. LMN and PQR are complementary
angles. Find the measures of the angles if
m LMN = (4x – 2)o
and m PQR = (9x + 1)o
.
ANSWER 26o
, 64o

12. 1.5
1 and 4 are a linear pair. 4 and 5
are also a linear pair.
ANSWER
Example 4
SOLUTION
To find vertical angles, look or angles formed by
intersecting lines.
To find linear pairs, look for adjacent angles whose
noncommon sides are opposite rays.
Identify all of the linear pairs and all
of the vertical angles in the figure at
the right.
1 and 5 are vertical angles.ANSWER

13. 1.5Example 5
SOLUTION
Let x° be the measure of one angle. The
measure of the other angle is 5x°. Then
use the fact that the angles of a linear
pair are supplementary to write an
equation.
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.
ALGEBRA

14. 1.5Example 5
SOLUTION
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.
ALGEBRA
xo
+ 5xo
= 180o
6x = 180
x = 30o
Write an equation.
Combine like terms.
Divide each side by 6.
The measures of the angles are 30o
and 5(30)o
= 150o
.
ANSWER

15. 1.5Guided Practice
ANSWER
No, no adjacent angles have their noncommon
sides as opposite rays, 1 and 4 , 2 and 5,
3 and 6, these pairs of angles have sides
that from two pairs of opposite rays.
Do any of the numbered angles in the diagram below
form a linear pair? Which angles are vertical angles?
Explain.
6.

16. 1.5Exit Slip
1. 1 and 2 are supplementary. If m 1 = 97 ,
find m 2.
o
2. 3 and 4 are complementary angles. If m 3= 74,
Find m 4.
o
ANSWER 83
o
ANSWER 16
o
3. Find m ABC.
ANSWER 36
o

17. 1.5
Homework
Pg 38-41
#18, 31, 42, 46, 58