Question

If the difference between two complementary angles is ${52}^{\circ }$, then the smaller angle is

• A. ${20}^{\circ }$
• B. ${19}^{\circ }$
• C. ${16}^{\circ }$
• D. ${17}^{\circ }$

Answer 1

The correct option is B ${19}^{\circ }$

Let the angle be $x^{\circ }$ and $y^{\circ }$, so
$x^{\circ }+y^{\circ }={90}^{\circ }\cdots \left(1\right)$
And
$x^{\circ }-y^{\circ }={52}^{\circ }\cdots \left(2\right)$
From equation $\left(1\right)$ and $\left(2\right)$, we get
$x={71}^{\circ },y={19}^{\circ }$