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Supplementary angles are two angles that add up to exactly 180 degrees (a straight line). The supplementary angles meaning is simple: when you combine these two angles, they form a perfect straight line. This fundamental concept appears everywhere in geometry, from basic angle relationships to advanced geometric proofs.
60° + 120° = 180°
These angles are adjacent (next to each other) and together form a straight line.
45° + 135° = 180°
These non adjacent supplementary angles are not touching each other but still add up to 180°. This shows that supplementary angles don't need to be next to each other to maintain their relationship.
Angle A + Angle B = 180°
The supplementary angles formula is simple: if one angle measures 70°, its supplementary angle must be 110° (since 70° + 110° = 180°). This formula works for any pair of supplementary angles.
When two angles form a linear pair, they are always supplementary.
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Master supplementary angles with these common problem types. Learn how to solve algebraic problems involving angles supplementary relationships.
“The larger of two supplementary angles exceeds by 18 degrees. Find both angles.”
Step 1: Let the smaller angle = x
Step 2: Then the larger angle = x + 18
Step 3: Since angles supplementary add to 180°:
x + (x + 18) = 180°
Step 4: Solve: 2x + 18 = 180°
2x = 162°
x = 81°
Answer: The angles are 81° and 99°
“Two supplementary angles are in the ratio 2:3. Find both angles.”
Step 1: Let the angles be 2x and 3x
Step 2: Since they are supplementary:
2x + 3x = 180°
Step 3: Solve: 5x = 180°
x = 36°
Step 4: Calculate both angles:
First angle = 2(36°) = 72°
Second angle = 3(36°) = 108°
Answer: The angles are 72° and 108°
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