Download Lesson 7-6a

7-6
6th grade math
Angle Pairs
Objective
• To find the measure of an unknown angle
from its relationship to other angles
• Why? To know how to ‘read’ angle pairs will
help you get a good foundation for geometry,
later in high school math.
California State Standards
MG 2.2
: Use the properties of complementary
and supplementary angles … to solve problems
involving an unknown angle.
MG 2.1: Identify angles as vertical, adjacent,
complementary, or supplementary and provide
descriptions of these forms.
AF 1.1
: Write and solve one-step linear
equations in one variable.
AF 3.2: Express in symbolic form simple
relationships arising from geometry.
• Vertical angles
Vocabulary
– Two angles formed by intersecting lines and having no sides
in common. They have the same angle ∠ m.
̮͡
• Supplementary angles
– Two angles whose sum of their measures equals 180°
• Complementary angles
– Two angles whose sum of their measures equals 90°
• Adjacent angles
– Two angles that have a common vertex and a common side
but do not overlap
.
Vocabulary
• Intersecting angles or lines
– Two lines or angles that have exactly one point in
common
• Perpendicular lines
– Two lines that intersect and form a 90° angle
┐
• Parallel lines
– Two lines that will never intersect each other
How to Find Measures of Angles w/o a Protractor
1) Observe and/or trace the
angles needed to be
identified: adjacent?,
supplementary?,
complementary?, vertical?
2) If vertical, the angles are
the same. If adjacent, are
angles supplementary or
complementary? If
supplementary, subtract
from 180°. If
complementary, subtract
from 90 °.
3) Check your work.
F 147° H
E
G
J
∠GEJ and ∠FEH are vertical angles
∠GEJ = 147 °, so ∠FEH = 147 °
If ∠GEH = 180°, ∠GEJ = 147 °, so ∠HEJ
= 180 - 147 = 33. ∠HEJ = 33°
Then ∠HEJ = 33°, so ∠GEF = 33°
How to Find Measures of Angles w/o a Protractor
N
C
50°
A O
D
∠AOC and ∠COD are adjacent,
supplementary angles, and
m∠COD = 50°. Find ∠AOC.
180 – 50 = 130
∠AOC = 130°
M
25°
L
K
∠KLM and ∠MLN are adjacent,
complementary angles and
m∠MLN = 25°. Find ∠KLM.
90 – 25 = 65
∠KLM = 65 °
1) 55, complementary
Try It!
Find the ∠m.
1)
a
2) 79, vertical
35°
3) 70, supplementary
2)
79°
4) 80, supplementary
b
3)
4)
110°
d
130°
50°
c
5) Draw: m∠ of 120° with an
adjacent supplementary
angle, name this angle.
5)
6) Draw: m∠ of 45° with an
adjacent, name this angle.
6)
7) Two angles that are
congruent and
supplementary. What are
their m∠ ?
60°
120°
45°
45°
7) 90° and 90°
Objective Review
• To find the measure of an
unknown angle from its
relationship to other
angles
• Why? You now know how to
‘read’ angle pairs will help you get
a good foundation for geometry,
later in high school math.
• Knowing the relationships of
certain pairs of angles can help you
find the measure of an unknown
angle.
Independent Practice
• Complete problems 819
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 20-22
• If still more time, work
on Accelerated Math.