How to Find Complementary and Supplementary Angles? (+FREE Worksheet!)
Complementary and supplementary angles – Example 2:
Complementary and supplementary angles – Example 3:
Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+43=180→x=180-43=137^\circ\)
Tutor-style math help
Supplementary, Complementary, and Vertical Angles: what to notice and how to work it
Geometry skill
Angle relationships let you solve unknown angles without measuring. The key is knowing which total the relationship creates.
What to notice first
Complementary angles total 90 degrees, supplementary angles total 180 degrees, and vertical angles are equal.
Common student mistake
Do not use 90 degrees for every angle pair. Supplementary and linear-pair situations use 180 degrees.
Key formulas and cues
\(\text{complementary: }a+b=90^\circ\)
\(\text{supplementary: }a+b=180^\circ\)
\(\text{vertical angles are equal}\)
A reliable path
- Label the diagramWrite each given measurement on the figure.
- Choose the formulaMatch the formula to distance, midpoint, area, volume, or angle relationships.
- Check unitsUse linear, square, or cubic units as appropriate.
Worked examples
Complementary angles
Example: One angle is \(37^\circ\). Find its complement.
- Complements total 90 degrees.
- Subtract 37 from 90.
- Label the angle.
Answer: \(53^\circ\)
Supplementary angles
Example: One angle is \(118^\circ\). Find its supplement.
- Supplements total 180 degrees.
- Subtract 118 from 180.
- Label the angle.
Answer: \(62^\circ\)
Try one before moving on
Try: Find the supplement of \(73^\circ\).
Answer: \(107^\circ\).
Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.
x
Supplementary, Complementary, and Vertical Angles: pop-up practice
Answer these quick questions, then use the feedback to decide which part of the lesson to review.
Choose an answer to begin.
1. Supplementary angles total:
2. The complement of 28 degrees is:
3. Vertical angles are:
Complementary and supplementary angles – Example 4:
Find the missing angle.
Solution:
Notice that two angles form a straight angle when together. This means that the angles are supplementary and have a sum of \(180^\circ\).
\(x+38=180→x=180-38=142^\circ\)
Exercises for Complementary and Supplementary Angles
Find the missing measurement in the pair of angles.
Find the missing measurement in the pair of angles.
1. \(\color{blue}{x=}\)
2.\(\color{blue}{x=}\)
3.\(\color{blue}{x=}\)
4.\(\color{blue}{x=}\)
5. The measure of an angle is \(31^°\). What is the measure of its complementary angle? __________
6. The measure of an angle is \(76^°\). What is the measure of its supplementary angle? __________
- \(\color{blue}{156^\circ}\)
- \(\color{blue}{15^\circ}\)
- \(\color{blue}{113^\circ}\)
- \(\color{blue}{46^\circ}\)
- \(\color{blue}{59^\circ}\)
- \(\color{blue}{104^\circ}\)
Original price was: $109.99.$54.99Current price is: $54.99.
Original price was: $109.99.$54.99Current price is: $54.99.
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