Question

Two complementary angles differ by $6^{\circ }$. Find the measure of the two angles.

Answer 1

Let the angles be x and y.
$,x+y={90}^{\circ }-\left(i\right)$
$andx-y=6^{\circ }-\left(ii\right)$
$Adding\left(i\right)and\left(ii\right),weget$
$\left(x+y\right)+\left(x-y\right)={90}^{\circ }+6^{\circ }$
$2x={96}^{\circ }$
$x={32}^{\circ }$
$Puttingthisvaluein\left(i\right),weget$
${32}^{\circ }+y={90}^{\circ }$
$y={58}^{\circ }$