Question
Two complementary angles differ by $20^\circ .$ Find the angles.
✓
Answer
Let one of the angle be $x,$
then other will be $x - 20.$
According to the question,
$x + (x - 20) = 90^\circ [\because$ sum of complementary angle is $90^\circ ]$
$\Rightarrow x + x - 20 = 90^\circ $
$\Rightarrow 2x - 20 = 90^\circ $
$\Rightarrow 2x = 90 + 20 [$transposing $(-20)$ to $RHS] $
$\Rightarrow 2x = 110^\circ $
$\Rightarrow\frac{2\text{x}}{2}=\frac{110^\circ}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=55^\circ$
Hence, the required angles are $55^\circ $ and $(55 - 20)^\circ $
i.e. $55^\circ $ and $35^\circ .$
then other will be $x - 20.$
According to the question,
$x + (x - 20) = 90^\circ [\because$ sum of complementary angle is $90^\circ ]$
$\Rightarrow x + x - 20 = 90^\circ $
$\Rightarrow 2x - 20 = 90^\circ $
$\Rightarrow 2x = 90 + 20 [$transposing $(-20)$ to $RHS] $
$\Rightarrow 2x = 110^\circ $
$\Rightarrow\frac{2\text{x}}{2}=\frac{110^\circ}{2} [$dividing both sides by $2]$
$\Rightarrow\text{x}=55^\circ$
Hence, the required angles are $55^\circ $ and $(55 - 20)^\circ $
i.e. $55^\circ $ and $35^\circ .$
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