1. Angles Relationships
Unit 7
Math 7

2. 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.

3. 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

4. Angle Relationships Supplementary Angles:
two angles whose measures add to 180°
Complementary Angles:
two angles whose measures add to 90°

5. Angle Relationships Example 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

6. Angle Relationships Example 3 – Find the measure of each angle
Angle HPM –
108 degrees
Angle JPI –
38 degrees

7. Angle Relationships Example 3 – Find the measure of each angle
Angle IPH –
34 degrees
Angle KPL –

8. Let’s Review Packet from Last week

9. EQ: How can we find missing angles using rules of geometry?

10. Find the complement of...
1) 20 70
2) 47 43
No complement
3) 100

11. Find the supplement of the given angle.
1) 40
140
5) 89 91
2) 18
162
6) 23
157
3) 153 27
7) 131 49
4) 65
115
8) 118 62

12. The easiest way to find the missing measure(s) of an angle is to set up an equation and solve. For example:

13. Complementary Angles sum is 90 . b a x+ 40 = 90 - 40 -40 x 40 x = 50
- Angles whose
sum is 90 . b a
x+ 40 = 90 x 40
x = 50

14. Supplementary Angles - Angles whose sum is 180o Find the value of x.30
x = 180
x = 150

15. (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) = 180
3x - 30 = 180
3x = 210 70
x = 70

16. Write a variable equation and solve.
Find an angle whose complement is 20
more than three times the angle.
x + 3x + 20 = 90 x
4x + 20 = 90
3x + 20
4x = 70
x = 17.5

17. Vertical Angles Theorem
- the opposite angles
of intersecting lines
must be equal.

18. What’s the relationship between angles a and b?
Vertical Angles Theorem
- the opposite angles
of intersecting lines
must be equal.
Find the missing angles a, b and c.
What’s the relationship between angles a and b? 25
155 b c a
155 25

19. Summary Name some ways in which we can find the
missing measure of an angle?

20. Independent Practice/HW