Download Aim #1 - Manhasset Schools

Aim #1: How do we solve for unknown angles?
CC Geometry H
Do Now: Determine the measure of the missing angles in the diagrams below and
explain what facts about angles you used.
A.
C.
B.
`
820
0
36
z
x0
0
y
0
1720
0
121
Two ≮s AOC and COB with a common side OC, are _______________ ≮s if C
belongs to the interior of ≮AOB.
The sum of angles on a straight line is 180° and two such ≮s are called a linear
pair. A linear pair of ≮s are two adjacent ≮s whose non-common sides form a
straight line.
Two ≮s are called supplementary if the sum of their measures is __________;
two ≮s are called complementary if the sum of their measures is __________.
Describing ≮s as supplementary or complementary refers only to the measures of
their ≮s; the positions of the ≮s or whether the pair of ≮s is adjacent to each
other is not part of the definition.
The total measure of the adjacent angles around a point is ________.
The total measure of the adjacent angles on one side of a line is______.
Find m ≮g:
Find m≮DCE:
B
A
720
E
C
D
Two ≮s are vertical if their sides form opposite rays.
(RT and RU are opposite rays, RV and RS are opposite rays.)Vertical ≮s have
_________ measure.
T
S
Find m ≮TRV:
R
520
V
U
Fill in the chart below using the diagrams given:
In the exercises below, AB, CD, and EF are line segments. Find the measure
of each marked angle or find the value of the given variables. Give reasons for your
calculations using the "Key Facts" handout. Show all thesteps to your solutions.
1.
≮a
= _____
2.
2.
≮b
= _____
D
C
C
B
E
F
A
y = ___________________
D
Let's sum it up!!!
• Adjacent angles are two angles with a common vertex and ray between them.
• Straight Angle: If two rays with the same vertex are distinct and collinear
(i.e. form a line), then each of the angles formed by the rays is called a straight
• A straight angle measures 180 .
• Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their
sides form two pairs of opposite rays.
0
• Complementary angles are two angles with a sum of 90 .
0
• Supplementary angles are two angles with a sum of 180 .
• A linear pair of angles are adjacent and supplementary.
0
≮.
KEY FACTS
Name ________________________
Date __________________
CC Geometry H
HW # 1
A
1. Use the following diagram to answer the questions below:
J
F
H
Z
G
a. Name an ≮ supplementary to ≮HZJ and provide the reason for your conclusion.
b. Name an ≮ complementary to ≮HZJ and provide the reason for your conclusion.
c. If m≮HZJ = 38, what is the measure of each of the following ≮s? Provide
reasons for your calculations.
(1)
(2)
(3)
2. Find the values of x and y. Give reasons for your calculations. Show all the
steps to your solutions.
c
B
y0
680
A
(4x ­ 2)0
300
D
OVER
3.
4.
C
D
A
x0
x0
y0
B
470
240
A
B
x0
C
D
5.
6.
A
D
A
(2x + 1)0
y0
C
(5x + 45)
0
(2x ­ 5)0
(3x ­ 25)0
D
E
(3x + 10)0
(y ­ 3)
B
F
0
y0
C
B