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Angles Relationships
Unit 7
Math 7
Angle Relationships – Warm UP
• Find the measure of angle 1 if the measure of angle 4 = 135o
• Angles 1 and 4 are
_______________ angles.• If they are supplementary
angles, they must add up
to _________degrees.
Angle Relationships
Let’s Review…• Adjacent Angles:
– two angles that share a vertex and a side but no points in their interiors.
• Vertical Angles:– angles formed by two intersecting lines, and are
opposite each other. Vertical angles are congruent.• Congruent Angles:
– angles that have the same measure
Angle Relationships
• Supplementary Angles:– two angles whose measures add to 180°
• Complementary Angles:– two angles whose measures add to 90°
Angle RelationshipsExample 2:• Find the measure of angles 2, 3, and 4 if 1 = 43o
• Angles 1 and 2 are
_______________ angles.• If they are supplementary
angles, they must add up
to 180 degrees.
Angle 2 measures 137 degrees.
supplementary
18043 x137x
Angle Relationships
Example 3 – • Find the measure of each angle
– Angle HPM – • 108 degrees
– Angle JPI – • 38 degrees
Angle Relationships
Example 3 – • Find the measure of each angle
– Angle IPH – • 34 degrees
– Angle KPL – • 34 degrees
Let’s Review Packet from Last week
EQ: How can we find missing angles using rules of geometry?
Find the complement of...
1) 20
2) 47
3) 100
70
43
No complement
Find the supplement of the given angle.
1) 40
2) 18
3) 153
4) 65
5) 89
6) 23
7) 131
8) 118
140
162
27
115
91
157
49
62
The easiest way to find the missing measure(s) of an angle is to set up an equation and solve.
For example:
Complementary Angles - Angles whose sum is 90 .
ab
ma + m b = 90
x40
x+ 40 = 90- 40 -40
x = 50
Supplementary Angles - Angles whose sum is 180o
Find the value of x.
x 30
x + 30 = 180- 30 - 30
x = 150
(Guided Practice) Write a variable equation and solve.
Find an angle whose supplement is 30 less than twice the angle.
x 2x - 30
x + (2x - 30) = 1803x - 30 = 180
+30 +303x = 210
x = 7070
Write a variable equation and solve.
Find an angle whose complement is 20more than three times the angle.
x3x + 20
x + 3x + 20 = 90
4x + 20 = 90- 20 -204x = 704 4
x = 17.5
Vertical Angles Theorem - the opposite anglesof intersecting linesmust be equal.
Vertical Angles Theorem - the opposite anglesof intersecting linesmust be equal.
Find the missing angles a, b and c.
25
a
bc
25
155
155
What’s the relationship between
angles a and b?
Name some ways in which we can find the missing measure of an angle?
Summary
Independent Practice/HW