Find the supplement of an angle (180° - x)
Step 1: Identify the Given Angle
Write down the measure of the angle for which you need to find the supplement.
Why: Supplementary angles always sum to 180°; you need the first angle to find the second.
Step 2: Verify Angle Is Between 0° and 180°
Check that 0 < α < 180. (Exactly 0° or 180° have no unique supplement.)
Why: Linear pairs and supplementary angles only exist within this range.
Step 3: Set Up the Supplementary Equation
α + β = 180°, where β is the unknown supplement.
Why: The definition of supplementary angles is that their measures sum to exactly 180°.
Step 4: Isolate the Supplement
Rearrange: β = 180° - α (subtract the given angle from 180).
Why: Algebraic rearrangement isolates the unknown angle.
Step 5: Verify the Result
Check that α + β = 180° and that β is between 0° and 180°.
Why: This confirms the calculation is correct and the result is geometrically valid.
Two angles are supplementary if the sum of their measures is exactly 180 degrees.
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