MCQ
An angle is $4$ time its complement. Find measure.
- A$42^\circ$
- B$62^\circ$
- C$52^\circ$
- ✓$72^\circ$
✓
Answer
Correct option: D.
$72^\circ$
If x is the angle, its complement will be $(90^\circ - x),$
because they have to add up to $90$, and here $x + (90^\circ - x) = 90^\circ $
$x$ is equal to $4$ times of its complement, so we have
$x = 4 \times (90^\circ - x)$
$\Rightarrow x = 360^\circ - 4x$
$\Rightarrow 5x = 360^\circ $
$\Rightarrow\ \text{X}=\frac{360^\circ}{5}$
$\Rightarrow\ \text{X}=72^\circ$
because they have to add up to $90$, and here $x + (90^\circ - x) = 90^\circ $
$x$ is equal to $4$ times of its complement, so we have
$x = 4 \times (90^\circ - x)$
$\Rightarrow x = 360^\circ - 4x$
$\Rightarrow 5x = 360^\circ $
$\Rightarrow\ \text{X}=\frac{360^\circ}{5}$
$\Rightarrow\ \text{X}=72^\circ$
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