MCQ
An angle is $14^\circ $ more than its complement. Find its measure.
- ✓$52^\circ$
- B$62^\circ$
- C$32^\circ$
- D$42^\circ$
✓
Answer
Correct option: A.
$52^\circ$
Let the angle $= x$
Its complement $= 90^\circ - x$
According to the question, $x$ is $14^\circ $ more than its complement,
$\Rightarrow x = (90^\circ - x) + 14^\circ $
$\Rightarrow x + x = 104^\circ $
$\Rightarrow 2x = 104^\circ $
$\Rightarrow\ \text{X}=\frac{104^\circ}{2}=52^\circ$
Its complement $= 90^\circ - x$
According to the question, $x$ is $14^\circ $ more than its complement,
$\Rightarrow x = (90^\circ - x) + 14^\circ $
$\Rightarrow x + x = 104^\circ $
$\Rightarrow 2x = 104^\circ $
$\Rightarrow\ \text{X}=\frac{104^\circ}{2}=52^\circ$
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