Question

Two complementary angles differ by$40$. Find the angles.

Answer 1

Two angles are complementary if their sum is$90°$.

Let the angles are $x$ and $y$

so, $x+y=90°$………(1)

so, complementary angle of $x$ is $90°-x$

and, complementary angle of $y$ is $90°-y$

Now, according to the question

Two complementary angles are differ by 40

$\Rightarrow \left({90}^0-x\right)-\left({90}^0-y\right)=40$

$\Rightarrow {90}^0-x-{90}^0+y=40$

$\Rightarrow y-x=40°$ ……….(2)

Adding (1) and (2) we get,

$2y=130°\Rightarrow y=65°$

put this value of y in (1) we get,

$x+65°=90°\Rightarrow x=25°$

hence angles are $65°,25°$