Lines and Angles — MATHS STD 7 — Question

 Let one of the angle be $x.$ Since, the difference between the two angles is $30^\circ $,
then the other angle will be $(x – 30^\circ ).$
Also, the two angles are complementary, so their sum is equal to $90^\circ .$
$\therefore\text{x}+\text{(x}-30^\circ)=90^\circ$
$\Rightarrow\text{x}+\text{x}-30^\circ=90^\circ$
$\Rightarrow2\text{x}=90^\circ+30^\circ$
$\Rightarrow2\text{x}=120^\circ$
$\Rightarrow\text{x}=\frac{120^\circ}{2}$
$\Rightarrow\text{x}=60^\circ$
$\therefore$ Required angles are $60^\circ $ and $(60^\circ - 30^\circ ),$ i.e. $60^\circ $ and $30^\circ $