Question

Find an angle which is two-thirds of its complement.

• A. ${36}^{\circ }$
• B. ${54}^{\circ }$
• C. ${18}^{\circ }$
• D. ${66}^{\circ }$

Answer 1

The correct option is A

${36}^{\circ }$

Let the required angle be $x^{\circ }$

Complement of $x^{\circ }=(90-x{)}^{\circ }$

$\Rightarrow x=\frac{2}{3}\times (90-x)$

$\Rightarrow 3x=180-2x$

$\Rightarrow 5x=180$

$\Rightarrow x={36}^{\circ }$