Download • Vertical angles have equal measure. • The sum of the adjacent

CC Geometry 10X
Aim #1: How do we solve for unknown angles?
Do Now: Classify the angle as acute, right, obtuse, or straight.
450
A
B
89.50
C
Points A, B, and C are collinear.
950
IMPORTANT FACTS ARE BOXED.
AS PART OF YOUR HOMEWORK EACH NIGHT, YOU ARE EXPECTED TO STUDY
AND LEARN ALL INFORMATION THAT IS BOXED.
A linear pair of angles are two adjacent angles whose non-common sides form
a straight line.
C
• Name the two angles that form a linear pair: _____ _____
• m≮AOC + m≮COB = _____ degrees.
A
o
O
B
Angles that form a linear pair sum to _____ .
o
Supplementary angles are two angles with a sum of _______ .
o
Complementary angles are two angles with a sum of _______ .
The sum of the adjacent
o
angles around a point is ______.
ao
The sum of the adjacent angles
o
on one side of a line is______.
bo co
o
eo d
bo
a
o
co do
eo
a + b + c + d + e = _____
a + b + c + d + e = _____
Summing it up...
Reasons used to justify measures of unknown angles (Aim 1)
• Angles that form a linear pair sum to 180 .
o
• Supplementary angles sum to 180 .
o
• Complementary angles sum to 90 .
o
• The sum of the adjacent angles around a point is 360.
o
• The sum of the adjacent angles on one side of a line is 180
.
o
• Vertical angles have equal measure.
Exercise Set A : Find x, and justify your answer using a sentence.
(1)
B
xo
x = _____
65o
A
≮A is complementary to ≮B.
(2)
C
x = _____
38o
xo
D
≮A is supplementary to ≮B.
x = _____
(3)
x0
1210
(4)
x = _____
x0
670
(5)
x = _____
x0
(6)
x = _____
720
x0
New Definition: Vertical angles are two angles formed by opposite rays.
Name a pair of opposite rays: ______ ______
Name a second pair of opposite rays. _____ ______
C
A
O
Name a pair of vertical angles. ≮______ ≮ _______
Name a second pair of vertical angles. ≮______ ≮ _______
Vertical angles have _________ measure.
D
B
Exercise Set B : Find the missing variables; write a sentence to justify your work.
(8)
(7)
xo
zo
yo
520
x = ____ y = ____ z = ____
b = ____ c = ____ d = ____
Exercise Set C : Find the missing variable; write a sentence to justify your work.
(10)
(9)
e = _____
a = _____
(12)
(11)
360
A
b = _____
400
c = _____
c
B
(13)
820
do
do
d = _______
(14)
eo
910
e
o
910
910
e = _______
eo
Exercise Set D : Find the missing variable(s) using an algebraic solution.
Write a sentence to justify your work.
(15)
850
xo
(2x)o
350
x = ________
D
A
(16)
(y + x)o
(2x)
o
(y ­ x)o
B
C
x = _______ y = _______
Exercise Set E : Find x using an algebraic solution.
Find the measures of the requested angles.
(17)
A
E
xo
G
C
m≮CGB = ______
m≮EGA = ______
m≮BGF = ______
m≮FGD = ______
D
(4x­10)o
x = ______
F
B
(18)
C
B
(3x+6)o
E
(x­10)o
G
F
(x­11)o
A
(19)
D
m≮EGA = ______
m≮DGF = ______
m≮CGB = ______
m≮AGD = ______
x = ______
A
B
F
C
E
x = ______
D
m≮EFD = ______
m≮BFC = ______
m≮AFE = ______
m≮AFB = ______
Let's Sum it Up!!
• Adjacent angles are two angles with a common vertex and ray between them.
• Angles that form a linear pair are supplementary (sum to 180 ).
o
• The sum of the adjacent angles on one side of a line is 180 .
o
• The sum of the adjacent angles about a point is 360 .
o
• A straight angle measures 180 .
0
• A right angle measures 90 .
o
• Vertical angles are equal in measure.
0
• Complementary angles are two angles with a sum of 90 .
• Supplementary angles are two angles with a sum of 180 .
0
• Angles that form a linear pair are supplementary (sum to 180 ).
o
KEY FACTS
Name ________________________
Date __________________
CC Geometry 10X
HW # 1 (Finding missing angles)
1. Study the boxed facts and "Let's Sum it Up" in Aim 1. (They will be used in this
homework.)
2. Use the diagram to the right to answer the questions below:
a. Name an angle supplementary to ≮HZJ and
provide the reason for your answer.
A
J
F
H
Z
G
b. Name an angle complementary to ≮HZJ and provide the reason for your answer.
c. If m≮ HZJ = 38, what is the measure of each of the following angles? Provide
reasons for your answer.
(1)
(2)
(3)
#3-7 Find the values of x and/or y. Show all the steps to your solution, and write
reasons for your results in sentence form.
3.
B
C
680
A
y0
(4x ­ 2)0
300
D
OVER
#4-5 Find missing variables and the requested angle measures.
F
4. 5.
E
C
D
x0
A
24
0
x0
470
B
E
x0
F
A
B
C
D
x = _____
m≮AED = _____
m≮DEB = _____
m≮CEB = _____
x = _____
m≮AFD = _____
m≮DFB = _____
m≮EFB = _____
#6-7 Find x and y using an algebraic solution. Write a sentence justifying each
equation you used.
6. AB and CD are line segments.
7. AB and EF are line segments.
C and D are not collinear points.
E
A
D
C
y0
(5x + 45)
0
(2x ­ 5)0
(3x ­ 25)
D
0
A
(2x+1)0
E
(3x+10)0
F
0
(y ­ 10)
yo
B
B
C