Question

Find the angles in each of the following.
The angle whose complement is one sixth of its supplement

• A. ${72}^{\circ }$
• B. ${32}^{\circ }$
• C. ${62}^{\circ }$
• D. None of these

Answer 1

Answer: (A)

${72}^{\circ }$

Let the angle be $\angle A$.

complement of an angle A is $90-\angle A$

supplement of that angle is ${180}^o-\angle A$

given the complement is $1/6$ th of supplement.

$=>{90}^o-A=\frac{1}{6}({180}^o-A)={30}^o-\frac{A}{6}$

$=>\frac{5A}{6}={60}^o$.

$=>A=\frac{{60}^o\times 6}{5}$.

solving that $A={72}^o$.