Geometry
GradesGrade 7GeometryAngle Relationships

Angle Relationships

📐 Geometry
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Angle Relationships

Complementary, supplementary, vertical, and adjacent angles follow reliable rules you can always count on.

Angles formed by intersecting lines and adjacent angles on a straight line follow predictable relationships. Knowing these relationships lets you find unknown angle measures without a protractor.

Key angle relationships:

Complementary: two angles that sum to 90°Supplementary: two angles that sum to 180°Vertical angles: opposite angles formed by two intersecting lines (always equal)Adjacent angles: angles that share a vertex and a side
∠A+∠B=90∘(complementary)\angle A + \angle B = 90^\circ \quad (\text{complementary})
∠A+∠B=180∘(supplementary)\angle A + \angle B = 180^\circ \quad (\text{supplementary})
✂ī¸Finding a missing angle
Two lines intersect. One angle is 65°. Find the other three angles.

Vertical angle = 65° (opposite)
Supplementary angles = 180° − 65° = 115° (adjacent)
Fourth angle (vertical to 115°) = 115°

Strategy for angle problems:

1Identify the relationship: complementary, supplementary, or vertical?
2Set up the equation using the angle sum rule
3Solve for the unknown angle
4Check that your angles add up to the expected total
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Remember This!

Memory trick: C comes before S in the alphabet, and 90 comes before 180. Complementary = 90°, Supplementary = 180°.

✏ī¸ Try It!

An angle measures 38°. What is the measure of its supplement?

Practice with CalcVerse
📐Angle RelationshipsâŦĄPolygon Angle Explorer
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