Download Vertical Angles

Seventh Grade
Geometry
Unit 4
MGSE7.G.5. Use facts about
supplementary, complementary,
vertical, and adjacent angles in a multistep problem to write and solve simple
equations for an unknown angle in a
figure.
Essential Question
How can I use the special angle
relationships – supplementary,
complementary, vertical, and adjacent – to
write and solve equations for multi-step
problems?
Types of Angles
Right, Acute, or
Obtuse
Two lines
that will
never
intersect
Two lines that
intersect
and form four
right angles
Opposite
angles that are
formed by
intersecting
lines.
These angles
are equal to
each other.
Two angles
that share a
common
ray.
Two angles
that add up
to 90°
Two angles
that add up
to 180°
Angle Style
Complementary Angles – angles that add up to 90º
Supplementary Angles – angles that add up to 180º
Complementary
20 + x = 90
-20 - 20
x = 70
Supplementary
115 + x = 180
-115
- 115
x = 65
How can I remember which
angle is which…
complementary or supplementary?
Linear Pair
Two adjacent angles that form a line. They
are supplementary. (angle sum = 180)
t
1+2=180
2+4=180
4+3=180
3+1=180
1 2
3 4
Supplementary Angles/
Linear Pair
Find the measures of the missing angles
t
108? 72 
72  108
? 
72 + x = 180
-72
-72
x = 108
Who uses this stuff?
Congruent Angles – Angles with equal measurement
A ≅ B means that A is congruent to B.
Adjacent Angles - angles that share a common vertex
and ray…angles that are back to back.
*Vertex – the “corner” of the angle
*Ray – a line that has an endpoint
on one end and goes on
forever in the other direction.
Vertical Angles
Two angles that are opposite angles at intersecting
lines. Vertical angles are congruent angles.
t
1 2
3 4
1   4
2   3
Vertical Angles
Hint: V and A are facing opposite directions
and are the same shape. Vertical Angles
are facing opposite each other and are the
same measurement.
Vertical Angles
Find the measures of the missing angles
t
125 
? 
125
55
? 
55 
Name the angles and write an equation to find the angle measurements.
3(15)
45°
complementary
45 + 3x = 90
-45
-45
3x = 45
÷3 ÷3
x = 15
supplementary
3x + 25 + 2x = 180
5x + 25 = 180
2(31)
62°
-25 -25
5x = 155
3(31)+25
÷5 ÷5
118°
x = 31
55°
55-20
35°
4(33.5)+5
139°
complementary
x + x – 20 = 90
2x – 20 = 90
+20 +20
2x = 110
÷2 ÷2
x = 55
supplementary
4x + 5 + 41 = 180
4x + 46 = 180
-46 -46
4x = 134
÷4 ÷4
x = 33.5
Name the angles and write an equation to find the angle measurements.
4•25-25
75°
7(20)
140°
vertical
4x - 25 = 75
+25 +25
4x = 100
÷4 ÷4
x = 25
supplementary
7x + x + 20 = 180
8x + 20 = 180
-20 -20
8x = 160
20+20
40°
÷8 ÷8
x = 20
complementary
4x + 2x = 90
6x = 90
÷6 ÷6
x = 15
4(15)
60°
2(15)
30°
complementary
69 + 2x -1 = 90
68 + 2x = 90
-68 -68
2x = 22
÷2
÷2
x = 11
2•11-1
21°
Closing
add up to 90°
• Complementary Angles ______________
add up to 180°
• Supplementary Angles ______________
are congruent
• Vertical Angles ____________________