Discussion
The measure of an angle for which the measure of the supplement is four times the measure of the complement is
Answer: C
The angle is 60°.
Let the angle be x. Its supplement is 180° - x and its complement is 90° - x. The supplement is four times the complement:
\[ \begin{aligned} 180 - x &= 4(90 - x) \\ 180 - x &= 360 - 4x \\ 3x &= 180, \quad x = 60 \end{aligned} \]
Check: the supplement is 120° and the complement is 30°, and 120 = 4 × 30. For 30° the ratio is 150 : 60, for 45° it is 135 : 45 = 3, and for 75° it is 105 : 15 = 7, so none of those works.
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