Mathematics

Which of the following statements is correct  ?


ANSWER

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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