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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

8 problems

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

Two angles are a linear pair. One angle measures 3x + 18 degrees and the other measures 150°. Find x and the unknown angle.

3x + 18°150°Schematic — use linear pair

Show reasoning / computation: __________________________________________

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.

4x + 14°146°Schematic — use linear pair

Show reasoning / computation: __________________________________________

Problem 3

Vertical angles are labeled 5x + 15 degrees and 50°. Find x and the unknown angle.

5x + 15°50°Schematic — use vertical

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.

2x + 11°157°Schematic — use supplementary

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.

2x + 11°69°Schematic — use the stated relationship

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.

4x + 13°33°Schematic — use the stated relationship

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.

5x + 15°40°Schematic — use the stated relationship

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.

2x + 10°60°Schematic — use the stated relationship

Show reasoning / computation: __________________________________________

Teaching note 1

Vertical angles are equal.

Teaching note 2

Complementary angles total 90°; supplementary and linear-pair angles total 180°.

Teaching note 3

Solve for x, then substitute back to find the requested angle measure.

Continue the 7.G progression

Move to another Grade 7 geometry skill

Open Grade 7 geometry hub →
Scale drawings: lengths & areas →Reproduce a scale drawing →Constructing triangles →Cross sections of 3D figures →Circle area & circumference →Composite area →Surface area & volume of right prisms →

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.