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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.

**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.

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.

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 FREEUse 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 FREEIn 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.**

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

2**Identify 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}.

3**Find the missing angle.**

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

x=180-17

x = 163

4**Clearly state the answer using angle terminology.**

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

\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}.

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}.

\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}.

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}.

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.

- 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.

**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}.

- Angles
- Acute angle
- Obtuse angle
- Right angle
- Adjacent angles
- Complementary angles
- Geometry theorems
- Vertical angle theorem
- Straight angle
- Angles point
- Pentagon angles

1. The two angles shown are supplementary. Find the measure of \angle pmn.

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}.

2. The two angles shown are supplementary. Which of the following could be the measure of \angle srt?

\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}.

2. \angle a and \angle b are supplementary angles. \angle a measures at 14^{\circ}. What is the measure of \angle b?

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}.

4. \angle f and \angle g are supplementary angles. \angle f measures at 113^{\circ}. What is the measure of \angle g?

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}.

5. Two angles 'x and y' are supplementary and one of them is 47^{\circ}. What is the size of the other angle?

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}.

6. Two angles 'x and y' are supplementary and one of them is 123^{\circ}. What is the size of the other angle?

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 add up to 180 degrees, or a straight angle.

Complementary angles add up to 90 degrees, or a right angle.

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

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

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