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