Angle Relationships
Grade 7 · Math · Study Guide
Identify and use relationships between angle pairs — complementary, supplementary, vertical, and adjacent — to find missing measures.
An angle is formed when two rays share the same endpoint, called the vertex. Angles are measured in degrees. A right angle measures exactly 90°, a straight angle is exactly 180°, a full rotation is 360°, and an acute angle is less than 90° while an obtuse angle is between 90° and 180°.
Two angles are complementary if their measures add up to 90°. If one angle is 35°, its complement is 90° − 35° = 55°. Two angles are supplementary if their measures add up to 180°. If one angle is 110°, its supplement is 180° − 110° = 70°. These relationships let you find missing angle measures using simple subtraction or algebra.
When two straight lines cross, they form two pairs of vertical angles. Vertical angles are the angles across from each other at the intersection — they are always equal in measure. Adjacent angles share a side and a vertex but do not overlap. When two lines cross, adjacent angles are supplementary.
Angles formed by parallel lines cut by a transversal have special relationships you will study more in 8th grade, but the basics start here. When a straight line (transversal) crosses two parallel lines, alternate interior angles are equal and corresponding angles are equal.
Angle relationships are everywhere in architecture, art, and engineering. Carpenters use them to cut corners accurately, and graphic designers use them to create symmetric patterns. Understanding angle pairs also builds the foundation for triangle geometry and proof-based reasoning in high school.
| Relationship | Condition | Key Property |
|---|---|---|
| Complementary | Two angles that sum to 90° | Each is the other's complement |
| Supplementary | Two angles that sum to 180° | Each is the other's supplement |
| Vertical angles | Formed by intersecting lines | Always equal in measure |
| Adjacent angles | Share a vertex and side | Side by side; may or may not sum to anything specific |
| Relationship | Given | Missing Angle | Work |
|---|---|---|---|
| Complementary | One angle = 42° | ? = 48° | 90 − 42 = 48 |
| Supplementary | One angle = 115° | ? = 65° | 180 − 115 = 65 |
| Vertical | One angle = 73° | ? = 73° | Vertical angles are equal |
| Adjacent on a line | One angle = 58° | ? = 122° | 180 − 58 = 122 |
Key terms
- Complementary angles
- Two angles whose measures sum to 90°
- Supplementary angles
- Two angles whose measures sum to 180°
- Vertical angles
- Opposite angles formed when two lines intersect; they are always equal
- Adjacent angles
- Two angles that share a vertex and a side but do not overlap
- Straight angle
- An angle that measures exactly 180°; it forms a straight line
Practice questions
Two angles are supplementary. One angle measures 68°. What is the measure of the other angle?
- 22°
- 112°
- 122°
- 68°
Show answer
Answer: 112°
Vertical angles formed by two intersecting lines are always equal.
Show answer
Answer: True
Two angles are complementary. One measures 34°. The other measures ___°.
Show answer
Answer: 56
Two lines intersect forming four angles. One angle is 130°. What is the measure of the adjacent angle?
- 130°
- 50°
- 90°
- 230°
Show answer
Answer: 50°
Complementary angles must each be less than 90°.
Show answer
Answer: True
Fun facts
- A boomerang's angle between its two arms is carefully designed using supplementary angle principles — change that angle and it will not return to the thrower.
- The ancient Greeks were so obsessed with angles and geometry that Euclid wrote 13 books about it around 300 BCE, and students still use those ideas today.
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