Supplementary Angles - Math Steps, Examples & Questions

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Supplementary angles

Here you will learn about supplementary angles, including how to find missing angles by applying knowledge of supplementary angles.

Students will first learn about supplementary angles as a part of measurement and data in 4th grade. They will expand that knowledge as they progress through middle school.

What are supplementary angles?

Supplementary angles are two angles that add up to $180$ degrees. They can be adjacent or not adjacent. Adjacent angles are angles that share a common arm and a vertex.

Adjacent supplementary angles	Non-adjacent supplementary angles

Adjacent supplementary angles make a straight line.

You can use what you know about supplementary angles to decompose angles and find the measurement of an unknown angle.

What are supplementary angles?

Common Core State Standards

How does this relate to 4th grade math?

Grade 4: Measurement and Data (4.MD.C.7)
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, for example, by using an equation with a symbol for the unknown angle measure.

[FREE] Angles Worksheet (Grade 4)

Use this quiz to check your grade 4 students’ understanding of angles. 10+ questions with answers covering a range of 4th grade angles topics to identify areas of strength and support!

DOWNLOAD FREE

[FREE] Angles Worksheet (Grade 4)

Use this quiz to check your grade 4 students’ understanding of angles. 10+ questions with answers covering a range of 4th grade angles topics to identify areas of strength and support!

DOWNLOAD FREE

How to find the measure of supplementary angles

In order to find the measure of supplementary angles you need to:

Determine which angles are supplementary.
Identify given angle measurements and the unknown angle or angles.
Find the missing angle.
Clearly state the answer.

Supplementary angles examples

Example 1: finding missing angle measures (adjacent angles)

The two angles shown are supplementary. Find the measure of angle $x.$

Determine which angles are supplementary.

The question states that angles $x$ and $y$ are supplementary and equal $180^{\circ}.$

$x+y=180$

2Identify given angle measurements and the unknown angle or angles.

Angle $y$ is $17^{\circ}.$

The unknown angle is angle $x,$ and when it’s added to $17^{\circ}$ will equal $180^{\circ}.$

3Find the missing angle.

To find the missing angle, you will subtract $17$ from $180.$

$x=180-17$

$x = 163$

4Clearly state the answer using angle terminology.

The measurement of angle $x$ is $163^{\circ}.$

Example 2: finding missing angle measures (adjacent angles)

$\angle ABC$ and $\angle CBD$ are supplementary angles. $\angle ABC$ has a measure of $109^{\circ}.$ What is the measure of $\angle CBD?$

Determine which angles are supplementary.

The question states that $\angle ABC$ and $\angle CBD$ are supplementary angles, which means they equal $180$ degrees.

$\angle A B C + \angle C B D=180^{\circ}$

Identify given angle measurements and the unknown angle or angles.

The question states that $\angle A B C=109^{\circ}.$

$\angle CBD$ is unknown, and can be called $x,$ and when added to $109^{\circ}$ will equal $180^{\circ}.$

$109+x=180$

Find the missing angle.

In order to find the measure of $\angle CBD,$ you will subtract $109$ from $180.$

$x=180-109$

$x=71^{\circ}$

Clearly state the answer.

The measurement of angle $CBD$ is $71^{\circ}.$

Example 3: finding missing angle (non-adjacent angles)

The pair of angles are supplementary. Find the measure of angle $F.$

Determine which angles are supplementary.

The question states that angles $D$ and $F$ are supplementary and equal $180^{\circ} .$

$D+F=180$

Identify given angle measurements and the unknown angle or angles.

Angle $D$ has a measurement of $21^{\circ}.$

The measurement of angle $F$ is unknown, but when added to angle $D,$ will equal $180^{\circ}.$

$21^{\circ}+F=180^{\circ}$

Find the missing angle.

In order to find the measure of the second angle, $\angle F,$ you will subtract $21$ from $180.$

$F=180-21$

$\angle F=159$

Clearly state the answer.

The measurement of $\angle F$ is $159^{\circ}.$

Example 4: finding missing angle (not adjacent)

$\angle L$ and $\angle M$ are supplementary angles. $\angle M$ measures at $98^{\circ}.$ What is the measure of $\angle L?$

Determine which angles are supplementary.

As stated in the question, $\angle L$ and $\angle M$ are supplementary angles, which means when added together will equal $180^{\circ}.$

$L + M=180^{\circ}$

Identify given angle measurements and the unknown angle or angles.

$\angle M$ measures at $98^{\circ}.$

The measurement of angle $L$ is unknown, but when added to $\angle M,$ will equal $180^{\circ}.$

$L+98^{\circ}=180^{\circ}$

Find the missing angle.

You will subtract $98$ from $180$ to find the measure of $\angle L.$

$L=180-98$

$L=82^{\circ}$

Clearly state the answer.

The measurement of $\angle L$ is $82^{\circ}.$

Example 5: finding missing angle (no diagram)

Two angles $‘x$ and $y'$ are supplementary and one of them is $147^{\circ}.$ What is the size of the other angle?

Determine which angles are supplementary.

The question states that angles $x$ and $y$ are supplementary angles, meaning when added together they will equal $180^{\circ}.$

$x+y=180^{\circ}$

Identify given angle measurements and the unknown angle or angles.

Because it is not stated which angle is $147$ degrees, you can assume that $\angle x= 147^{\circ}.$

This would mean that $\angle y$ is unknown, but when added to $\angle x$ would equal $180^{\circ}.$

$147^{\circ}+y=180^{\circ}$

Find the missing angle.

You will subtract $147$ from $180$ to find the measure of $\angle y.$

$y=180-147$

$y=33^{\circ}$

Clearly state the answer.

The measurement of $\angle y$ is $33^{\circ}.$

Example 6: finding missing angle

Two angles $‘x$ and $y'$ are supplementary and one of them is a right angle. What is the size of the other angle?

Determine which angles are supplementary.

The question states that angles $x$ and $y$ are supplementary, meaning when added together they will equal $180^{\circ}.$

$x+y=180^{\circ}$

Identify given angle measurements and the unknown angle or angles.

Because it is not stated which angle is a right angle, you can assume that $\angle x$ is a right angle. A right angle will always measure at $90^{\circ}.$

This would mean that $\angle y$ is unknown, but when added to $\angle x$ would equal $180^{\circ}.$

$90^{\circ}+y=180^{\circ}$

Find the missing angle.

You will subtract $90$ from $180$ to find the measure of $\angle y.$

$y=180-90$

$y=90^{\circ}$

Clearly state the answer.

The measurement of $\angle y$ is $90^{\circ}. \; \angle y$ is also a right angle.

Teaching tips for supplementary angles

Rather than having students practice finding and decomposing supplementary angles on multiple skill worksheets, provide them with a variety of practice problems, activities, and/or projects that have a real-world context. This will deepen their understanding of this skill.

Easy mistakes to make

Mixing up supplementary angles and complementary angles
Students may mix up supplementary and complementary angles, thinking that complementary angles sum to $180^{\circ}$ and that supplementary angles sum to $90^{\circ}.$ However, complementary angles have a sum of $90^{\circ}$ and supplementary angles have a sum of $180^{\circ}.$

Assuming supplementary angles must have a common vertex
Supplementary angles can be either adjacent or not adjacent. Not adjacent supplementary angles do not share a common vertex, but their angles will still add up to $180^{\circ}.$

Practice supplementary angles questions

x=112^{\circ}

x=56^{\circ}

x=106^{\circ}

x=65^{\circ}

The two angles are supplementary, so they must have a sum of $180.$

You will subtract $124$ from $180$ to find the measure of the missing angle.

$x=180-124$

$x=56$

The missing angle measures at $56^{\circ}.$

\angle srt=45^{\circ}

\angle srt=114^{\circ}

\angle srt=90^{\circ}

\angle srt=10^{\circ}

$\angle srt$ is an acute angle, which means that it’s measurement is less than $90^{\circ}.$

An angle with the measure of $114^{\circ}$ would be an obtuse angle. $\angle srt$ can not equal $114^{\circ}.$

An angle with the measure of $90^{\circ}$ would be a right angle. $\angle srt$ is not a right angle.

An angle with the measure of $10^{\circ}$ would be an acute angle, however, it would be a very skinny acute angle. $\angle srt$ is too large to equal $10^{\circ}.$

$\angle srt$ is an acute angle, with a measurement of $45^{\circ}.$

b=76^{\circ}

b=166^{\circ}

b=83^{\circ}

b=114^{\circ}

The two angles are supplementary, so they must have a sum of $180.$

You will subtract $14$ from $180$ to find the measure of the missing angle.

$b=180-14$

$b=166$

The missing angle measures at $166^{\circ}.$

113^{\circ}

23^{\circ}

77^{\circ}

67^{\circ}

The two angles are supplementary, so they must have a sum of $180.$

You will subtract $113$ from $180$ to find the measure of the missing angle.

$g=180-113$

$g=67$

The missing angle measures at $67^{\circ}.$

43^{\circ}

133^{\circ}

47^{\circ}

313^{\circ}

The two angles are supplementary, so they must have a sum of $180.$

You will subtract $47$ from $180$ to find the measure of the missing angle.

$x=180-47$

$x=133$

The missing angle measures at $133^{\circ}.$

53^{\circ}

123^{\circ}

57^{\circ}

237^{\circ}

The two angles are supplementary, so they must have a sum of $180.$

To find the measure of the missing angle, you can subtract $123$ from $180.$

$x=180-123$

$x=57$

The missing angle measures at $57^{\circ}.$

Supplementary angles FAQs

What’s the difference between complementary and supplementary angles?

Supplementary angles add up to $180$ degrees, or a straight angle.
Complementary angles add up to $90$ degrees, or a right angle.

Can three angles be supplementary?

No, three angles will never be supplementary, even if the sum of their measurement is $180^{\circ}.$ Supplementary angles will only occur in pairs.

Is there a formula for supplementary angles?

$\angle a + \angle b = 180^{\circ};$ two angles are supplementary if $angle \; a$ and $angle \; b$ equal $180^{\circ}.$

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