Mathematics

# Which of the following statements is correct  ?

Bisectors of the adjacent angles forming a linear pair form a right angle.

##### SOLUTION
Two angles form a linear pair if they have;
A common arm
A common vertex
Their interiors do not overlap.
The sum of two angles is ${180}^{\circ}$.
$\therefore,$ linear pair of angles are adjacent angles whose non-common arms are opposite rays.
Thus,option$(a)$ is false
If one of the angle is acute then the other must be obtuse to form a straight angle by the definition of linear pair.
So option$(b)$ and $(c)$ are false
we know that linear pair of angle is $180$ degrees.
A line, ray or segment which cuts another line segment into two equal parts is a line bisector.
And it is given that they are bisecting the adjacent angles  forming a linear pair .
so,$\dfrac{{180}^{\circ}}{2}={90}^{\circ}$
Hence each angle should be ${90}^{\circ}$. And we  know that ${90}^{\circ}$ is known as right angle .hence option$(d)$ is correct.

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Single Correct Medium Published on 09th 09, 2020
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