Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
Question
The supplement of an acute angle is ________ .
✓
Answer
As the sum of the supplementary angles is $180^\circ .$
Let one of the angle measure $x^\circ ,$ such that $x < 90.$
Let the other angle measures $y^\circ .$ As the angles are supplementary there sum is $180^\circ .$
$x + y = 180^\circ ...(1) $
$x < 90^\circ ...(2)$
Now subtracting $(1)$ from $(2) -y < -90^\circ y > 90^\circ $
Then, other angle y is clearly an obtuse angle. Illustration: Let the given acute angle be $30^\circ $
Then, the other angle becomes $(180 - 30)^\circ = 150^\circ $
This is clearly an obtuse angle.
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