complementary and supplementary angles assignment edgenuity quizlet

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Course: 7th grade   >   Unit 9

• Angles: introduction
• Name angles
• Complementary & supplementary angles
• Vertical angles
• Identifying supplementary, complementary, and vertical angles
• Complementary and supplementary angles (visual)
• Complementary and supplementary angles (no visual)

Complementary and supplementary angles review

• Vertical angles are congruent proof
• Finding angle measures between intersecting lines

Complementary angles

Supplementary angles, practice set 1: identify complementary and supplementary angles.

• (Choice A)   Complementary angles A Complementary angles
• (Choice B)   Supplementary angles B Supplementary angles
• (Choice C)   None of the above C None of the above

Practice set 2: Find a missing angle measure

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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• Math Article
• Complementary Angles Supplementary Angles

Supplementary And Complementary Angles

Supplementary angles and complementary angles are defined with respect to the addition of two angles. If the sum of two angles is 180 degrees then they are said to be supplementary angles , which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

When two line segments or lines meet at a common point (called a vertex), at the point of intersection an angle is formed. When a ray is rotated about its endpoint, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position.

In fig. 1 if the ray OP is rotated in the direction of the ray OQ, then the measure of its rotation represents the angle formed by it. In this case, the measure of rotation which is the angle formed between the initial side and the terminal side is represented by Ɵ.

Complementary Angles

When the sum of two angles is 90°, then the angles are known as complementary angles . In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Here we say that the two angles complement each other.

How to Find Complementary Angles?

Suppose if one angle is x then the other angle will be 90 °  – x. Hence, we use these complementary angles for trigonometry ratios , where one ratio is complementary to another ratio by 90 degrees such as;

• sin (90° – A) = cos A and cos (90° – A) = sin A
• tan (90° – A) = cot A and cot (90° – A) = tan A
• sec (90° – A) = cosec A and cosec (90° – A) = sec A

Hence, you can see here the trigonometric ratio of the angles gets changed if they complement each other.

In the above figure, the measure of angle BOD is 60 ° and angle AOD measures 30 ° . By adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary angles.

The following angles in Fig. 3 given below are complementary to each other as the measure of the sum of both the angles is 90 ° . ∠POQ and ∠ABC are complementary and are called complements of each other.

For example: To find the complement of 2x + 52°, subtract the given angle from 90 degrees.

90 o  –  (2x + 52 o ) =  90 o  – 2x – 52 o   = -2x + 38 o  

The complement of 2x + 52 o is 38 o  – 2x.

Supplementary Angles

When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles .

How to Find Supplementary Angles?

The two angles form a linear angle, such that, if one angle is x, then the other the angle is 180 ° – x. The linearity here proves that the properties of the angles remain the same. Take the examples of trigonometric ratios such as;

• Sin (180 – A) = Sin A
• Cos (180 – A) = – Cos A (quadrant is changed)
• Tan (180 – A) = – Tan A

In Fig. 4 given above, the measure of ∠AOC is 60 o and ∠AOB measures 120 o . By adding both of these angles we get a straight angle. Therefore, ∠AOC and ∠AOB are supplementary angles, and both of these angles are known as a supplement to each other.

Also, learn:

• Adjacent Angles Vertical
• Lines And Angles

Difference between Complementary and Supplementary Angles

How to remember easily the difference between Complementary angles and supplementary angles?

• “ C “  letter of  C omplementary stands for “ C orner” (A right angle,  90 ° )
• “ S “   letter of  S upplementary stands for “ S traight” ( a straight line, 180 ° )

Video Lesson on Types of Angles

Solved Examples

The example problems on supplementary and complementary angles are given below:

Find the complement of 40 degrees.

Solution:  

As the given angle is 40 degrees, then,

The complement is 50 degrees.

We know that sum of complementary angles =  90 degrees

So, 40°  + 50°  = 90°

Find the supplement of the angle 1/3 of 210°.

Step 1: Convert 1/3 of 210° 

That is, (1/3) x 210° = 70°

Step 2: Supplement of 70° = 180° – 70° = 110°

Therefore, the supplement of the angle 1/3 of 210° is 110°

Example 3:  

The measures of the two angles are (x + 25)° and (3x + 15)°. Find the value of x if angles are supplementary angles. 

We know that, Sum of Supplementary angles =  180 degrees

(x + 25)° + (3x + 15)° = 180°  

4x + 40°   = 180°  

4x = 140°  

x = 35°    

The value of x is 35 degrees.

The difference between the two complementary angles is 52°. Find both the angles.

Let, First angle = m degrees, then,

Second angle =  (90 – m)degrees   {as per the definition of complementary angles}

Difference between angles = 52° 

 (90° – m) – m = 52° 

90° – 2m = 52° 

 – 2m = 52° – 90°

Again, second angle = 90° – 19°   = 71°  

Therefore, the required angles are 19°, 71°.

Practice Questions

• Check if 65° and 35° are complementary angles.
• Are 80° and 100° supplementary?
• Find the complement of 54°.
• Find the supplement of 99°.
• If one angle measures 50° and is supplementary to another angle. Then find the value of another angle. Also, state what type of angle it is?

Frequently Asked Questions – FAQs

What are complementary angles give example., what are supplementary angles give examples., how to find complementary angles, what is the complementary angle of 40 degrees, how to find supplementary angles.

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My question is in Maths Class 7 : “What is the supplement of 2x-13?”

Supplementary angles sum up to 180 degrees. Therefore, 2x-13 = 180 2x = 180+13 x = 193/2 x = 96.5 degrees

What is the complementary angle of 60° ?

The complementary angle of 60° is 30° 60°+30° = 90°

What is the complement of 40°

The complement of 40° is 50° Since 90° – 40° = 50°

Let x and y are the two angles, supplementary to each other. As per the statement, say, y = 2x Therefore, x+y = 180 degrees (supplementary angles) x+2x = 180 3x = 180 x = 180/3 = 60 Hence, x = 60 degrees, y = 2x = 2(60) = 120 degrees

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Complementary and Supplementary Angles Worksheets

Utilize our printable complementary and supplementary angles worksheets to help build your child's skill at identifying complementary and supplementary angles, finding the unknown angles, using algebraic expressions to find angular measures, and more. A highly effective practice tool for grade 6, grade 7, and grade 8, these resources lay a firm foundation for the topic of complementary and supplementary angles. Make use of our free samples and subscribe for instant access to a potpourri of pdf worksheets.

Finding Complementary Angles - Type 1

This complementary angles worksheet requires kids to solve diverse exercises in 3 sections. Students must use the property that the sum of complementary angles is 90° to obtain their answers correctly.

• Download the set

Finding Complementary Angles - Type 2

The name of the game is identifying complementary angles. In this 6th grade exercise, identify the correct complementary pair by inference, match the complementary angles, and answer our in-out boxes.

Finding Unknown Angles in a Complementary Pair

Learn to find the unknown measure of each complementary angle with these worksheets. 7th grade kids keenly observe the right angles and equate them accordingly to find the measure of the unknown angle.

Algebra in Complementary Angles | One-Step & Two-Step

Find the unknown value of complementary angles using only an angle measure and an algebraic expression. Practice evaluating the expression to find the unknown values in one step or two steps.

Finding Supplementary Angles - Type 1

This supplementary angles worksheet drives kids to find the pair whose sum does/doesn't equal 180°, match the angles that form supplementary angles when added, and complete in/out boxes.

Finding Supplementary Angles - Type 2

Get your students to skillfully find supplementary pairs, match the angles, and follow the rules of the given in-out box for correct answers! Reiterate how two supplementary angles make a straight angle.

Finding Unknown Angles in a Supplementary Pair

Make finding the unknown measure of each supplementary angle a super-easy task! Observe the angles in each illustration and equate them accordingly to find the measure of the unknown angles.

Algebra in Supplementary Angles | One-Step & Two-Step

This part of our complementary and supplementary angles worksheets helps 7th grade and 8th grade students to use the fundamental property of supplementary angles and solve for x in either one or two steps.

Identifying Complementary and Supplementary Angles - Type 1

Inspire 6th grade and 7th grade children to find the complementary and supplementary angles for a given set of problems. Also, match the complement and supplement of the angles with this pdf set.

Identifying Complementary and Supplementary Angles - Type 2

Let your competence in identifying complementary and supplementary angles progress steadily. Identify the correct pairs by inference, find the measure of the angles, and answer the in-out boxes with precision.

Finding Unknown Angles in a Complementary or Supplementary Pair

Train students to keenly observe the right angles and straight angles and equate them to find the measure of the unknown angle in these printable complementary and supplementary angles worksheets.

Complementary and Supplementary Pairs | Adjacent and Non-Adjacent Angles (Multiple Rays)

Ready to demonstrate greater skills in finding the complementary and supplementary angles? Every pdf here contains 8 image-specific questions that test your understanding of multiple rays.

Algebra in Complementary and Supplementary Angles | One-Step & Two-Step

A right or straight angle with an angle measure and an algebraic expression is given. 7th grade and 8th grade students must set up the equation, perform inverse operations and solve for x in 1 or 2 steps.

Related Worksheets

» Pairs of Angles

» Angles Formed by a Transversal

» Linear Pairs of Angles

» Angles Around a Point

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Complementary and Supplementary Angles

6th - 7th grade, mathematics.

20 questions

Introducing new   Paper mode

No student devices needed.   Know more

• 1. Multiple Choice Edit 2 minutes 5 pts What are complementary angles? Angles that add up to 180° Angles that add up to 90°
• 4. Multiple Choice Edit 2 minutes 5 pts What are supplementary angles? Angles that add up to 180° Angles that add up to 90° Angles that are equal to each other Angles that are opposite of each other when lines intersect
• 10. Multiple Choice Edit 2 minutes 1 pt If ∠C and ∠D are supplementary, and the measure of ∠D is 45°, what is the measure of ∠C? 135 45 125 90
• 11. Multiple Choice Edit 2 minutes 1 pt If ∠A and ∠B are supplementary, and the measure of ∠A is 120°, what is the measure of ∠B? 180 50 60 80
• 12. Multiple Choice Edit 2 minutes 1 pt If ∠K and ∠S are complementary, and the measure of ∠K is 58°, what is the measure of ∠S? 122 22 110 32

THe three angles inside a triangle add up to

180 degrees

360 degrees

Which type of angle is this?

Which one is an acute angle?

Work out the size of the missing angle

Without using a protractor, find the measure of angle x.

214 degrees

186 degrees

Practice 1a: Name a pair of complementary angles

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Complementary and Supplementary Angles Calculator

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How does the complementary and supplementary angles calculator work, what 2 formulas are used for the complementary and supplementary angles calculator, what 4 concepts are covered in the complementary and supplementary angles calculator, example calculations for the complementary and supplementary angles calculator.

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