Download 1. The sum of two numbers is 90 and one number is 4 times the

1.5 Angle Relationships
September 08, 2010
Bell Ringers – Sept 7
1. The sum of two numbers is 90 and one number is 4 times
the other. Write the equation and solve to find the numbers.
2. In the diagram, MN bisects ∠PMQ and m∠PMQ = 122º.
Find m∠PMN. Illustrate with a picture. Classify ∠PMN.
3. M is the midpoint of the segment. Find EM.
•
8x - 6
7x
E
G
M
4. Find the coordinates of the midpoint of the segment with
the given endpoints.
P(-8, -7) and Q(11, 5)
1.5 Angle Relationships
September 08, 2010
1.5 Angle Relationships
Complementary angles - two angles whose sum is 90º
• Each angle is the
Supplementary angles - 2 angles whose sum is 180º
• Each angle is the
Complementary and supplementary angles can be
Adjacent angles - 2 angles that share a common vertex and
common side.
3
1
4
2
7
5
6
8
1.5 Angle Relationships
September 08, 2010
Ex 1: What is the complement and supplement of each angle?
a) 34º
b) 66º
Ex 2: Use the diagram to the right to answer the following
questions.
a) Name a pair of supplementary angles
2 3
b) Name a pair of complementary angles
1
5 4
c) Name a pair of adjacent angles
Ex 3: Find x and y.
•
N
(5x+30)º
(4x+15)º P (3y-15)º
O
(3y+15)º
•
L
•
M •
Guided Practice
1. Given that ∠1 is a complement of ∠2 and m∠1=8º,
find m∠2.
2. ∠LMN and ∠PQR are complementary angles. Find
the measures of the angles if m∠LMN = (4x - 2)º and
m∠PQR = (9x + 1)º.
3. Two roads intersect to form supplementary angles,
∠XYW and ∠WYZ. Find m∠XYW and m∠WYZ.
•W
•
X
(2x + 14)º
(4x - 20)º
Y
•
Z
1.5 Angle Relationships
September 08, 2010
vertical angles: 2 ∠s whose sides form 2 pairs of opposite rays.
linear pair: 2 adjacent ∠s whose noncommon sides form
opposite rays.
1
2
3
6
5
4
Ex 4: Use the diagram to answer the following
a) Are ∠1 and ∠2 a linear pair?
b) Are ∠4 and ∠5 a linear pair?
2
1
3
5 4
a) Are ∠5 and ∠3 vertical angles?
Ex 5: T and V are supplementary. The measure of T is
half of the measure of V. Find the measure of each
angle.
Guided Practice
5. Two angles form a linear pair. The measure of one angle is
5 times the measure of the other. Find the measure of each
angle.
Homework
Pages 38-41 #1, 2, 4-7, 9-15 odd, 16, 17-27 odd, 30-54
even, 57
1.5 Angle Relationships
September 08, 2010