An angle is \(\frac{3}{7}\) times its supplementary angle. Find the angle.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 54°
Two angles are supplementary when they add up to \(180^\circ\), so the supplement of an angle \(x\) is \(180^\circ-x\).
The angle \(x\) is \(\frac{3}{7}\) of its supplement: \(x=\frac{3}{7}(180^\circ-x)\)
\(7x=540^\circ-3x\)
\(10x=540^\circ\), so \(x=54^\circ\)
Shortcut: The angle and its supplement are in the ratio \(3:7\), so they share \(180^\circ\) in 10 parts: the angle is \(\frac{3}{10}\times180^\circ=54^\circ\).