Gujarat BoardEnglish MediumSTD 7MATHSLines and Angles1 Mark
MCQ
The angle that is three times as large as its complement is:
A
$135^\circ $
✓
$67.5^\circ$
C
$50.5^\circ$
D
$45^\circ$
✓
Answer
Correct option: B.
$67.5^\circ$
Let the measure of the angle be $x$ degrees.
Since it is given that the angle is three times as large as its complement, it means
$x = 3 (90 - x)$
$\Rightarrow x = 270 - 3x$
$\Rightarrow x + 3x = 270$
$\Rightarrow 4x = 270$
$\Rightarrow\text{x}=\frac{270}{4}$
$\Rightarrow x = 67.5$
Therefore, the measure of the angle is $67.5^\circ .$
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