Math Skill: Angle Measurements

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Angle Measurements

Review the definition of complementary, supplementary, and vertical angles here.

An easy way to remember complementary and supplementary:
Complementary angles form a corner.
Supplementary angles form a straight line.

Complementary Angles

If two angles add up to 90°, they are complementary. You can also say that one angle is the complement of the other angle.
Complementary angles do not need to be next to each other.

Examples

Solve for the missing angle.

a. What is the complement of an angle that measures 50°? °

Let x = measure of the complement angle.
The two angles add up to 90°.
x + 50° = 90°

x = 90° - 50° = 40°

The complement angle measures 40°.

b. ∠A and ∠B are complementary angles. If m∠A = 23°, what is m∠B? °

Complementary angles add up to 90°.
m∠A + m∠B = 90°

23° + m∠B = 90°

m∠B = 90° - 23° = 67°

Supplementary Angles

If two angles add up to 180°, they are supplementary. You can also say that one angle is the supplement of the other angle.
Supplementary angles do not need to be next to each other.

Examples

Solve for the missing angle.

a. What is the supplement of an angle that measures 50°? °

Let x = measure of the supplement angle.
The two angles add up to 180°.
x + 50° = 180°

x = 180° - 50° = 130°

The supplement angle measures 130°.

b. If m∠B = 135°, what is m∠A? °

∠A and ∠B form a straight angle, which measures 180°. This means that ∠A and ∠B are supplementary angles.
m∠A + m∠B = 180°

m∠A + 135° = 180°

m∠A = 180° - 135° = 45°

Vertical Angles

When two lines intersect, they create two pairs of vertical angles. Vertical angles are opposite each other and are equal.

Vertical angles share a vertex.
(Vertex is the point where lines meet.)

Examples

Solve for the missing angle(s).

a. ∠A and ∠B are vertical angles. If m∠A = 39°, what is m∠B? °

Vertical angles are equal.
m∠A = m∠B

39° = m∠B

b. In the figure below, two lines intersect to form ∠A, ∠B, ∠C, and ∠D.

If m∠B = 66°, find the missing angles.
m∠A = °
m∠C = °
m∠D = °

∠A and ∠B are supplementary because they form a straight line.
m∠A + m∠B = 180°

m∠A + 66° = 180°

m∠A = 180° - 66° = 114°

∠A and ∠C are vertical angles.
m∠A = m∠C

114° = m∠C

∠B and ∠D are vertical angles.
m∠B = m∠D

66° = m∠D

Complexity=1, Mode=comp

Solve for the missing angle(s).
Figures are not drawn to scale.

1. If m∠A = 43°, what is m∠B?

m∠B = °

2. What is the complement of an angle that measures 33°? °

Complexity=1, Mode=supp

Solve for the missing angle(s).
Figures are not drawn to scale.

1. ∠A and ∠B are supplementary angles. If m∠B= 50°,
what is m∠A? °

2. What is the supplement of an angle that measures 60°? °

Complexity=1, Mode=vert

Solve for the missing angle(s).
Figures are not drawn to scale.

1. In the figure below, two lines intersect to form ∠A,
∠B, ∠C, and ∠D.

If m∠C = 60°, what is m∠A? °

2. ∠A and ∠B are vertical angles. If m∠B= 165°,
what is m∠A? °

Complexity=1

Solve for the missing angle(s).
Figures are not drawn to scale.

1. What is the complement of an angle that measures 63°? °

2. In the figure below, two lines intersect to form ∠A,
∠B, ∠C, and ∠D.

If m∠D = 145°, find the missing angles.
m∠A = °
m∠B = °
m∠C = °

Answers

Complexity=1, Mode=comp

Solve for the missing angle(s).
Figures are not drawn to scale.

Problem

Correct Answer

Your Answer

If m∠A = 43°, what is m∠B?

m∠B = °

Solution
∠A and ∠B are complementary angles which means they add up to 90°.

m∠A + m∠B	=	90°
m∠B	=	90° - m∠A
m∠B	=	90° - 43° = 47°

#	Problem	Correct Answer	Your Answer
2	What is the complement of an angle that measures 33°?	°
Solution Complementary angles add up to 90°.

Complexity=1, Mode=supp

Solve for the missing angle(s).
Figures are not drawn to scale.

Problem

Correct Answer

Your Answer

∠A and ∠B are supplementary angles. If m∠B= 50°,
what is m∠A?

Solution
∠B and ∠A are supplementary angles which means they add up to 180°.

m∠B + m∠A	=	180°
m∠A	=	180° - m∠B
m∠A	=	180° - 50° = 130°

#	Problem	Correct Answer	Your Answer
2	What is the supplement of an angle that measures 60°?	°
Solution Supplementary angles add up to 180°.

Complexity=1, Mode=vert

Solve for the missing angle(s).
Figures are not drawn to scale.

Problem

Correct Answer

Your Answer

In the figure below, two lines intersect to form ∠A,
∠B, ∠C, and ∠D.

If m∠C = 60°, what is m∠A?

Solution
∠C and ∠A are vertical angles which means they are equal.
m∠C = m∠A = 60°

#	Problem	Correct Answer	Your Answer
2	∠A and ∠B are vertical angles. If m∠B= 165°, what is m∠A?	°
Solution ∠B and ∠A are vertical angles which means they are equal. m∠B = m∠A = 165°

Complexity=1

Solve for the missing angle(s).
Figures are not drawn to scale.

#	Problem	Correct Answer	Your Answer
1	What is the complement of an angle that measures 63°?	°
Solution Complementary angles add up to 90°.

Problem

Correct Answer

Your Answer

In the figure below, two lines intersect to form ∠A,
∠B, ∠C, and ∠D.

If m∠D = 145°, find the missing angles.

m∠A = °
m∠B = °
m∠C = °

Solution

∠D and ∠A are supplementary angles which means they add up to 180°.

m∠D + m∠A	=	180°
m∠A	=	180° - m∠D
m∠A	=	180° - 145° = 35°

∠D and ∠B are vertical angles which means they are equal.
m∠D = m∠B = 145°

∠D and ∠C are supplementary angles which means they add up to 180°.

m∠D + m∠C	=	180°
m∠C	=	180° - m∠D
m∠C	=	180° - 145° = 35°