Question

Find the angles in each of the following.
The angles whose supplement is four times its complement

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${120}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${60}^{\circ }$

Find the angle whose supplement is 4 times its complement

Let say Angle $=X°$

Supplement angle$=180°-X°$

Complement Angle $=90°-X°$

supplement is 4 times its complement

$=>180°-X°=4\ast (90°-X°)$

$=>180°-X°=360°-4X°$

$=>3X°=180°$

$=>X°=60{}^o$.