📐 Supplementary Angles Calculator
Calculate supplementary angles (angles that sum to 180°)
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How to Use This Calculator
Enter Angle(s)
Option A: Enter one angle to find its supplement. Option B: Enter both angles to check if they are supplementary.
Calculate
Click "Calculate Supplementary Angle" to find the result.
Review Result
See the supplementary angle or verify if the two angles are supplementary (sum to 180°).
Formula
Angle 1 + Angle 2 = 180°
Supplementary Angle = 180° - Given Angle
Definition:
Two angles are supplementary if their sum equals 180 degrees (π radians).
Examples:
- 120° + 60° = 180° → Supplementary
- 90° + 90° = 180° → Supplementary
- 150° + 30° = 180° → Supplementary
- 100° + 70° = 170° → NOT supplementary (sum is not 180°)
Finding the Supplement:
If one angle is known, its supplement is: Supplement = 180° - Known Angle
- If angle = 120°, supplement = 180° - 120° = 60°
- If angle = 45°, supplement = 180° - 45° = 135°
- If angle = 90°, supplement = 180° - 90° = 90°
Special Cases:
- Straight angle (180°) has no supplement (would be 0°)
- Angles greater than 180° cannot have supplements in standard geometry
- Two equal supplementary angles: 90° + 90° = 180° (right angles)
About Supplementary Angles Calculator
The Supplementary Angles Calculator finds angles that sum to 180 degrees. Supplementary angles form a straight line when placed adjacent to each other, and are fundamental in geometry, especially in parallel lines and linear pairs.
When to Use This Calculator
- Geometry: Solve problems involving supplementary angles
- Parallel Lines: Find angles formed by parallel lines and transversals
- Linear Pairs: Calculate angles in linear pairs
- Education: Learn and practice angle relationships
- Engineering: Design components with specific angle requirements
- Construction: Ensure proper angles in building projects
Why Use Our Calculator?
- ✅ Flexible Input: Find supplement or verify two angles
- ✅ Instant Results: Calculate immediately
- ✅ Clear Verification: Shows if angles are supplementary
- ✅ Educational: Helps understand angle relationships
- ✅ 100% Accurate: Precise calculations
- ✅ Completely Free: No registration required
Understanding Supplementary Angles
Supplementary angles are two angles whose measures add up to exactly 180 degrees:
- Straight Line: When supplementary angles are adjacent, they form a straight line (180°).
- Linear Pair: Two adjacent supplementary angles form a linear pair, sharing a common side and forming a straight line.
- Parallel Lines: When parallel lines are cut by a transversal, consecutive interior angles and same-side interior angles are supplementary.
- Not the Same as Complementary: Complementary angles sum to 90°, while supplementary angles sum to 180°.
- Can Be Non-Adjacent: Supplementary angles don't need to be adjacent; they just need to sum to 180°.
Real-World Applications
Parallel Lines: In geometry, when two parallel lines are intersected by a transversal, same-side interior angles are supplementary.
Architecture: Architects use supplementary angles when designing structures with specific angle relationships, especially in parallel and perpendicular elements.
Navigation: Supplementary angles help in calculating bearings and course corrections in navigation and surveying.
Frequently Asked Questions
What are supplementary angles?
Supplementary angles are two angles that add up to exactly 180 degrees. Examples include 120° and 60°, or 90° and 90°.
What's the difference between supplementary and complementary angles?
Supplementary angles sum to 180°, while complementary angles sum to 90°. Both are important angle relationships, but they serve different purposes in geometry.
Do supplementary angles have to be adjacent?
No, supplementary angles don't need to be adjacent. They just need to sum to 180°. However, when they are adjacent, they form a linear pair and create a straight line.
What is a linear pair?
A linear pair consists of two adjacent supplementary angles. They share a common side and form a straight line (180°).
How do I find the supplement of an angle?
Subtract the angle from 180°: Supplement = 180° - Angle. For example, the supplement of 120° is 180° - 120° = 60°.
Are supplementary angles always in straight lines?
When supplementary angles are adjacent, they form a straight line. However, non-adjacent supplementary angles exist as well - they just need to sum to 180°.
What are some common supplementary angle pairs?
Common pairs include: 120° and 60°, 150° and 30°, 135° and 45°, 90° and 90°, 100° and 80°. Note that 90° and 90° are equal supplementary angles (both are right angles).
How are supplementary angles used with parallel lines?
When parallel lines are cut by a transversal, same-side interior angles are supplementary. This property is fundamental in proving parallel line theorems and solving geometry problems.