Question

Two complementary angles differ by ${20}^{\circ }$. Find the measure of the angle.

Answer 1

Let the two angles be $x$ and $y$.

If the sum of the two angles is ${90}^{\circ }$ then they are said to to be complementary angles.

$\Rightarrow x+y={90}^{\circ }$---(1)

It is given that, angles are differ by ${20}^{\circ }$.

$\Rightarrow x-y={20}^{\circ }$---(2)

add (1) and (2)

$\Rightarrow x+y+x-y={90}^{\circ }-{20}^{\circ }$

$\Rightarrow 2x={110}^{\circ }$

$\Rightarrow x=\frac{{110}^{\circ }}{2}$

$\Rightarrow x={55}^{\circ }$

Now, substitute $x={55}^{\circ }$ in $x+y={90}^{\circ }$

$\Rightarrow {55}^{\circ }+y={90}^{\circ }$

$\Rightarrow y={90}^{\circ }-{55}^{\circ }$

$\Rightarrow y={35}^{\circ }$

Hence, the required angles are ${55}^{\circ }$ and ${35}^{\circ }$.