Download How to Find the Missing Angle Measure

FINDING MISSING ANGLE
MEASURES
part 1
LEARNING TARGET 2
 Use the definitions and relationships of complementary,
supplementary, adjacent, and vertical angles to determine
missing angle measures.
VERTICAL ANGLES
Let’s Review…Vertical Angles are not adjacent, are
formed by two intersecting lines, and are congruent
(equal).
Angles A and B are Vertical and therefore the same
angle measure.
VERTICAL ANGLES
We can use the definition of Vertical Angles to find the
measures of other angles.
How to Find the Missing Angle Measure :
All vertical angles are congruent (equal) and therefore equal to
each other.
If Angle A is 35°, then Angle B is also 35 °.
VERTICAL ANGLES
Find the angle measure of each missing angle.
COMPLEMENTARY ANGLES
Let’s Review…Complementary Angles are two angles whose
sum is 90°.
b
a
ma + m b = 90
COMPLEMENTARY ANGLES
How to Find the Missing Angle Measure :
Calculate the measure of the missing angle so that the sum of
the two angles equals 90 °.
27° + b = 90°
b = 63°
COMPLEMENTARY ANGLES
Find the measure of the missing angle.
SUPPLEMENTARY ANGLES
Let’s Review…Supplementary Angles are two (or more) angles
whose sum is 180°.
a
b
mamb 180
SUPPLEMENTARY ANGLES
How to Find the Missing Angle Measure :
Calculate the measure of the missing angle so that the sum of
the two angles equals 180°.
155° + b = 180°
b = 25°
SUPPLEMENTARY ANGLES
Find the measure of the missing angle.
SUPPLEMENTARY ANGLES
Find the Supplement of each angle.
Angle
Supplement
Your Angle + X = 180°
50°
130°
110°
70°
65°
115°
26°
154°
COMPLEMENTARY ANGLES
Find the Complement of each angle.
Angle
Complement
Your Angle + X = 90°
50°
40°
110°
Impossible
65°
25°
26°
64°
TIME TO PRACTICE
1)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
36°
1)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
36°
Relationship: Complementary
90° – 36° = 54°
2)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
64°
2)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
64°
Relationship: Complementary
90 ° – 64° = 26°
5)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
168
°
5)
Find
theMISSING
missingANGLE
angle.
FIND
THE
?°
168
°
Relationship: Supplementary
180° – 168° = 12°
6)
Find
theMISSING
missingANGLE
angle.
FIND
THE
58°
?°
6)
Find
theMISSING
missingANGLE
angle.
FIND
THE
58°
?°
Relationship: Supplementary
180° – 58° = 122°
FIND THE MISSING ANGLE
?º
35º
FIND THE MISSING ANGLE
?º
35º
Relationship: Vertical
35° = 35°
FIND THE MISSING ANGLE
?º
140º
FIND THE MISSING ANGLE
?º
140º
Relationship: Vertical
140° = 140°
FINDING A MISSING
ANGLE AND X
Part 2
FINDING THE MISSING ANGLE…WITH X.
 Sometimes the lines between Geometry and Algebra blur just a
bit. For example, sometimes the missing angle is not just a
letter but a problem to be solved. Let’s take a look.
We know that the two angles are supplementary…but how do we
solve for X.
When we solve these types of problems we are going to have T WO
ANSWERS…what does X equal and what is the measure of the
missing angle.
FIND THE MISSING ANGLE AND X
 We begin by figuring out what the two angles need to equal when added
together. In this case…180°
Angle 1 + Angle 2 = 180
30 + 2x = 180
(We can solve this…no problem)
2x = 150
X = 75
So the angle is 2x = 2(75) =
150°
Solve for
x. AND X
FIND THE3)
MISSING
ANGLE
2x°
3x°
What is the relationship? What do the two terms need to equal?
Solve for
x. AND X
FIND THE3)
MISSING
ANGLE
2x°= 2(18) =
36°
2x°
3x° = 3(18) =
54°
3x°
3x° + 2x° = 90°
5x = 90
x =18
Solve for
x. AND X
FIND THE7)
MISSING
ANGLE
4x°
5x°
What is the relationship? What do the two terms need to equal?
Solve for
x. AND X
FIND THE7)
MISSING
ANGLE
5x° = 5(20) =
100°
4x° = 4(20) =
80°
4x°
4x° + 5x° = 180°
9x° = 180°
x = 20
5x°
Solve for
x. AND X
FIND THE8)
MISSING
ANGLE
X = 30
2(30) + 10 = 70°
2x + 10
(2x + 10) + (3x + 20) = 180
5x + 30 = 180
5x = 150
x = 30
X = 30
3(30) + 20 = 110°
3x + 20
Combine Like Terms
Solve for X
Solve for
x. AND X
FIND THE4)
MISSING
ANGLE
x + 25
2x + 5
What is the relationship? What do the two terms need to equal?
Solve for
x. AND X
FIND THE4)
MISSING
ANGLE
X = 20
20 + 25= 45
x + 25
X = 20
2(20) + 5 = 45
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20
2x + 5
Combine Like Terms
Solve for X
FIND THE MISSING ANGLE AND X