Question

Question 90

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

Answer 1

Let one of the angle be x, then other will be x - 20.
According to the question,
x + (x - 20) = ${90}^{\circ }[\because sumofcomplementaryanglesis{90}^{\circ }$
$\Rightarrow x+x-20={90}^{\circ }\Rightarrow 2x-20={90}^{\circ }\Rightarrow 2x=90+20\left[transposing\right(-20\left)toRHS\right]\Rightarrow 2x={110}^{\circ }\Rightarrow \frac{2x}{2}=\frac{{110}^{\circ }}{2}\left[dividingbothsidesby2\right]\Rightarrow x={55}^{\circ }$
Hence, the required angles are ${55}^{\circ }$ and $(55-20{)}^{\circ }$ i.e. ${55}^{\circ }and{35}^{\circ }$