Angles Main Packet

Angles page #1
1. Angle: two rays with the same endpoint. The endpoint is called the vertex.
An angle is named by the vertex: ∠A
Vertex
A
X
An angle can also be named by three letters with
the vertex in the middle position.
Y
Z
∠XYZ or ∠ZYX
2. There are several ways to name an angle.
B
∠2 A number inside the angle.
∠A The point at the vertex.
A
2
C
∠BAC or ∠CAB Three letters - middle letter names
the vertex, other letters name a point from each
side.
Problems:
1.
K
1. Name the vertex of the angle.
L
3
J
2. What rays are the sides of the angle?
3. Give three other names for ∠LJK.
2. Three angles with their vertices at L are shown. The name ∠L cannot be used
because it would not be clear which angle was meant. Name the following angles with
three letters:
∠1 = __________
∠2 = __________
The remaining angle: __________
O
N
2
1
M
L

The Protractor: A protractor is an instrument used to measure angles.
Problems:
1. Measure the following angles:
A. B.
Angles page #2
C. D.
2. Draw angles with the measures given:
A. 42° B. 133°

3. Measure angles A through G.
Angles page #3
C
A
B
∠A + ∠B + ∠C = _____________________________
E
F
D
G
∠D + ∠E + ∠F + ∠G = ____________________________

Notes, Notes, Notes
1. A. Acute Angle: Measure is less than 90°.
Angles page #4
Draw an acute angle:
B. Right Angle: Measure is 90°.
Draw a right angle:
C. Obtuse Angle: Measure is between 90° and 180°.
Draw an obtuse angle:
D. Straight Angle: Measure is 180°.
Draw a straight angle:
2. Adjacent Angles: Two angles in a plane that have a common vertex and a common
side but no common interior points.
∠1 and ∠2 are adjacent angles
∠3 and ∠4 are not adjacent angles
2 1
1
2
3
4
3
4
3
4

Problems:
Angles page #5
1.
C
D
A
B
E
A. Name 4 different pairs of adjacent angles.
__________ and __________
__________ and __________
__________ and __________
__________ and __________
B. Name two different acute angles. __________ and __________
C. Name one obtuse angle. __________
D. Name two different right angles. __________ and __________
3. Perpendicular Lines (⊥ lines): Two lines that form equal adjacent (90°) angles.
Draw two lines that are perpendicular:
4. Complementary angles are two angles whose measures have the sum 90°. Each
angle is called a complement of the other.
Draw two angles that are complementary:

5. Supplementary angles are two angles whose measures have the sum 180°. Each
angle is called a supplement of the other.
Draw two angles that are supplementary:
Angles page #6
6. Angles of a Linear Pair:
A. The exterior sides of a linear pair of angles form a straight angle.
D
A B C
∠ABD and ∠DBC are a linear pair, the measure of ∠ABC is 180°.
∠ABD and ∠DBC are supplementary
∠ABD +∠DBC = 180°
Problems:
1.
∠1 + ∠2 + ∠3 = _________________
1
2
3

2.
Angles page #7
C
D
A
B
E
A. Name 2 different pairs of supplementary angles.
__________ and __________
__________ and __________
B. If CB is perpendicular to AE:
1. Name two different right angles. __________ and __________
2. Name a pair of complementary angles. _________ and __________
3. The measure of an angle is 8 times the measure of its supplement. Find the measure
of each angle.
4. The measure of an angle is 5 times the measure of its supplement. Find the measure
of each angle.

Angles page #8
5. The measure of an angle is 2 times the measure of its complement. find the
measure of each angle.
6. The measure of an angle is 5 more than 4 times the measure of its supplement. find
the measure of each angle.
7. The measure of an angle is 24 more than the measure of its complement. Find the
measure of each angle.
8. The measure of an angle is 20 less than 4 times the measure of its supplement. Find
the measure of each angle.

Angles page #9
9. Two angles are equal and complementary. What is the measure of each?
10. Use your protractor to draw the following:
A. Two adjacent complementary angles, one that has the measure 42°.
B. Two adjacent supplementary angles, one that has the measure 42°.

11.
Angles page #10
1 2
A. Write a formula (equation) for∠1 and ∠2: ___________________________
B. If ∠1 = 2x+3 and ∠2 = x-6, then: x = __________
∠1 = __________
∠2 = __________
C. If ∠1 = 3x-4 and ∠2 = 2x+9, then:
x = __________
∠1 = __________
∠2 = __________
12.
1
2
3
A. If ∠1 = 37° and ∠2 = 45° then ∠3 = __________
B. if ∠1 + ∠3 = 108°, then ∠2 = __________

13.
Angles page #11
2
1
A. Write a formula (equation) for ∠1 and ∠2: __________________________
B. If ∠1 = 3x+6 and ∠2 = 4x, then:
x = __________
∠1 = __________
∠2 = __________
C. If ∠1 = 2x-4 and ∠2 = x-2, then:
x = __________
∠1 = __________
∠2 = __________
14. Find the measure of each numbered angle.
48°
1
101° 2
3
104°
4 5
∠1 = __________ ∠2 = __________ ∠3 = __________
∠4 = __________
∠5 = __________

Angles page #12
Vertical Angles
∠3 and ∠4 are a pair of vertical angles.
They have no common side.
3 4
They are formed by two intersecting lines.
Vertical angles are equal.
Problems:
1.
Z
V
1
U
5
4
2
3
Y
W
X
A. ∠2 and ∠ __________ form a vertical pair.
B. Do ∠1 and ∠3 form a vertical pair? ________
C. Do ∠1 and ∠4 form a vertical pair? ________
D. What angle forms a vertical pair with ∠1? _______
2. Find the measures of angles 1 through 7.
4
1
106°
79°
42°
3
2
59°
7
67°
41°
6
5
∠1 = _______ ∠2 = _______ ∠5 = _______
∠3 = _______
∠6 = _______
∠4 = _______
∠7 = _______

3. Find x and the measure of each angle:
A.
Angles page #13
8x
10x-30
B.
x+45
2x
C.
6x
10x-32
D.
3x
x+18

4.
Angles page #14
D
A
4
3
1
B
2
C
A. Name two pairs of vertical angles:
__________ and __________
E
__________ and __________
B. The angle vertical to ∠DBE is __________.
C. Name 4 pairs of supplementary angles:
__________ and __________
__________ and __________
__________ and __________
__________ and __________
D. If ∠CBE = 42°, then: ∠ABD = __________
∠ABC = __________
∠DBC = __________
5. Find x and the measure of each angle.
A. B. C.
3x+20 5x 5x-18 90-4x
4x
5x-27

Proving that Vertical Angles are Equal
A theorem is a statement that you can prove.
Theorem: Vertical Angles are equal.
Angles page #15
1
3
4
2
Prove:
∠1 = ∠2 and ∠ 3 = ∠4

Angles page #16
Review complementary and supplementary Word Problems
1. Two angles are complementary and one angle is 4 times as large as the other angle.
Find the number of degrees in each angle.
2. The measure of an angle is 4 more than the measure of its supplement. Find the
measure of each angle.
3. The measure of an angle is 8 times the measure of its complement. Find the
measure of each angle.
4. The measure of an angle is 8 more than the measure of its complement. Find the
measure of each angle.
5. Two angles are supplementary. One angle is twice the other. find the number of
degrees in each angle.