Let the measure of the unknown angle be \( x \) degrees. The supplementary angle, which adds up to 180° with the angle \( x \), can be expressed as \( 180° - x \).
According to the problem, the angle \( x \) measures 36° less than its supplementary angle. This can be written as an equation:
\[ x = (180° - x) - 36° \]
Now, simplify the equation:
\[ x = 180° - x - 36° \] \[ x = 144° - x \]
Next, add \( x \) to both sides to combine like terms:
\[ x + x = 144° \] \[ 2x = 144° \]
Now, divide both sides by 2 to solve for \( x \):
\[ x = \frac{144°}{2} = 72° \]
Now that we know the measure of the unknown angle \( x \), we can find its supplementary angle:
\[ 180° - x = 180° - 72° = 108° \]
Thus, the measures of the angles are:
- The unknown angle: \( 72° \)
- Its supplementary angle: \( 108° \)
To recap:
- The unknown angle measures 72°
- Its supplementary angle measures 108°
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