Question

Two complementary angles differ by $12$degrees, find the angles.

Answer 1

Finding the angles:

Let one of the angles be$x.$

the two complementary angles differ by $12°$

So, bigger angle $=(x+12).$

Sum of Complementary angles $=90°$

$\begin{array}{rcl}& \Rightarrow & \mathrm{x}+\mathrm{x}+12°=90°\\ & \Rightarrow & 2\mathrm{x}+12°=90°\\ & \Rightarrow & 2\mathrm{x}=(90–12)°\\ & \Rightarrow & 2\mathrm{x}=78°\\ & \Rightarrow & \mathrm{x}=\frac{78°}{2}\\ & \Rightarrow & \mathrm{x}=39°\end{array}$

Smaller angle will be $39°$

Bigger angle $(x+12)=39°+12°=51°$

Therefore the angles are $39°,51°$ degrees respectively.