Question

An angle is ${30}^{\circ }$ more than half of its complement. Find the angle.

• A. ${150}^{\circ }$
• B. ${75}^{\circ }$
• C. ${60}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is D

${50}^{\circ }$

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

Its complement $=(90-x{)}^{\circ }$

$\Rightarrow x=\frac{1}{2}\times (90-x{)}^{\circ }+{30}^{\circ }$

$\Rightarrow 2x=90-x+60$

$\Rightarrow 2x+x=150$

$\Rightarrow 3x=150$

$\Rightarrow x={50}^{\circ }$