Download Angle Measures

Identifying and
Classifying Angles
Objective:
I can identify different types of angles and
calculate missing angles
Angle: a figure formed by two rays
with a common endpoint
DCE
ECD
C
1
E
1
D
Ways to name
this angle
ray
C
Vertex
Types of Angles
Right Angle
exactly 90°
Obtuse Angle
90° ˃ x ˂ 180°
Acute Angle
0° ˃ x ˂ 90°
How do you remember which is which?
Write down your method of remembering
angle types.
What is a straight angle?
180°
Guess what!
A straight angle is a straight line.
• Supplementary Angles:
2 angles that form 180 degrees
40 + 140 = 180
What does 180 degrees look like?
What would 90 degrees look like?
• Complementary Angles:
2 angles that form 90 degrees.
30 + 60 = 90
What does that square represent?
A 90° angle
• Vertical Angles:
Angles formed by two intersecting lines and
are on opposite sides of each other.
*Vertical angles are congruent. Angles
with equal
measures
Angle A and angle B are vertical.
Angle C and angle D are also vertical.
•Adjacent Angles:
2 angles that are next to each other,
they share a common side.
1 2
Angles 1 and 2 are adjacent angles.
•Adjacent Angles:
How would you describe this diagram using
the term adjacent angles?
Angle A and Angle C are adjacent.
Angle B and Angle D are adjacent.
Angle C and Angle B are adjacent.
Angle D and Angle A are adjacent.
There’s actually a shortcut when
people read or write angles!
• Just like “did not” is the same as
“didn’t”:
• The “measure of angle A” can be
written as “m∠A”.
How do you read“∠A” and “∠B”?
Angle A and Angle B
If angle 1 is 65 degrees, calculate
angle 2 and classify what type of
angle they form.
Angle 2 = ____25°____
These two angles form
_Complementary_ angles.
Calculate angles x and y and
classify the types of angles they
each form.
Angle x = ____25°______ Angle y = ___65°_______
Both sets of angles form Complementary angles.
Calculate angle x and classify what
kind of angle x + 130° forms.
Angle x = __50°___
Angle x + 130° form
___Supplementary_ angles.
There are 2 angles here.
• Is saying ∠O sufficient? Explain.
Saying ∠O is not sufficient
because ∠O is really the full 90°
You would identify
these two angles as
∠AOB and ∠ BOC
Calculate m∠AOB.
70°
Given ∠MNO has a value of 68.2°,
calculate ∠ONP and
classify the angle they form.
∠ ONP = 21.8°
The two angles
form
Complementary
angles.
o
In the diagram, m ∠8 = 72 .
Find the measures of ∠5, ∠6, ∠7.
5
8
6
7
o
m∠5 = 108
o
m∠6 = 72
o
m∠7 = 108
o
3x - 35
2xo
Calculate the angle measures.
What kind of angle do the two angles form together?
Supplementary Angles
What is the total measure of the two angles?
Thus: 3x - 35 + 2x = 180 Substitute “x” into the original expressions
3(43)
–
35
=
94
5x - 35 = 180
2(43) = 86
5x = 215
x = 43 The two angles measure
o
o
94 86
Write and solve an equation to find the
measures of the two angles below.
13x + 11x + 60 = 180
24x + 60 =180
24x = 120
x=5
o
13(5) = 65
o
11(5) + 60 = 115
If ∠𝐴 and ∠𝐵 are complementary, and m ∠𝐴
is five times m ∠𝐵, what is the m ∠𝐵?
Write an equation
Combine like terms
Divide both sides by 6
x + 5x = 90
6x = 90
x = 15
The m ∠𝐵 = 15
o
∠𝐴 and ∠𝐵 are complementary,
m ∠𝐴 = 2x + 30
m ∠𝐵 = 4x
What are the measures of ∠𝐴 and ∠𝐵?
2x + 30 + 4x = 90
6x + 30 = 90
6x = 60
x = 10
2(10) + 30 = 50
4(10) = 40
o
Measure of ∠𝐴 = 50
o
Measure of ∠𝐵 = 40
Write down as many statements using
math terms as you can in 2 minutes.
Supplementary Angles
and Adjacent Angles
A and B, B and D
Vertical Angles D and C, C and A
A and D
E and F, F and H
C and B
H and G, G and E
E and H
G and F
Alternate Exterior Angles
A and H, B and G
Alternate Interior Angles
C and F, E and D