Two angles are a linear pair. One angle measures 3x + 18 degrees and the other measures 150°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
CCSS 7.G.B.5 · angle facts + algebraic equations
Angle Relationships and Equations Worksheet Generator
Use angle relationships to write and solve an equation for x, then report the actual angle measure. Every known angle and algebraic expression is constructed from a valid solution first, so the diagram labels and answer key stay consistent.
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Angle Relationships & Equations
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
Two angles are a linear pair. One angle measures 4x + 14 degrees and the other measures 146°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 3
Vertical angles are labeled 5x + 15 degrees and 50°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 4
Two angles are supplementary. One angle measures 2x + 11 degrees and the other measures 157°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 5
Two angles are complementary. One angle measures 2x + 11 degrees and the other measures 69°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 6
Two angles are complementary. One angle measures 4x + 13 degrees and the other measures 33°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 7
Two angles are complementary. One angle measures 5x + 15 degrees and the other measures 40°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Problem 8
Two angles are complementary. One angle measures 2x + 10 degrees and the other measures 60°. Find x and the unknown angle.
Show reasoning / computation: __________________________________________
Using angle relationships to write and solve equations
Complementary angles add to 90 degrees, supplementary angles add to 180 degrees, and vertical angles formed by two crossing lines are equal. Write an equation from the relationship, solve for the variable, and then substitute to find the angle measures. Check that the angles add up as expected.
Worked examples
- Two supplementary angles are x and 2x + 30. Then x + 2x + 30 = 180, so 3x = 150 and x = 50. The angles are 50° and 130°.
- Two complementary angles are x and 3x + 10. Then 4x + 10 = 90, so x = 20 and the angles are 20° and 70°.
- Vertical angles measure (4x − 10)° and 70°. They are equal, so 4x − 10 = 70, giving x = 20.
Common slips
- Using 180 for complementary angles, or 90 for supplementary angles.
- Treating adjacent angles as vertical angles. Only the angles across from each other are equal.
- Stopping at the value of x. The question usually asks for the angle measures, so substitute back.
How to use this worksheet
Ask students to draw and label the angles before writing the equation, and to check that the final angles satisfy the relationship. The answer key gives each angle measure.
Common Core connection
- 7.G.B.5 · Use facts about supplementary, complementary, and vertical angles to solve problems.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Teaching note 1
Vertical angles are equal.
Teaching note 2
Complementary angles total 90°; supplementary and linear-pair angles total 180°.
Teaching note 3
Example: if a linear pair has one angle (3x + 10)°, set (3x + 10) + other = 180, solve for x, then substitute to get each measure.
Teaching note 4
Solve for x, then substitute back to find the requested angle measure.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Frequently asked questions
Do these include variables in angle measures?
Yes. Each item pairs a valid angle relationship with a linear expression such as 3x + 7.
Are the diagrams drawn to exact angle measure?
The labels are mathematically exact; the diagrams are controlled schematics so students must use the relationship rather than measuring the picture.
Which standard does this practice?
CCSS 7.G.B.5: use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple equations for an unknown angle.