Question

Which of the following statements is correct ?

• A. If two angles forming a linear pair, then each of these angle is of measure${90}^{\circ }$
• B. Angles forming a linear pair can be acute angle.
• C. Both of the angles forming a linear pair can be obtuse angle.
• D. Bisectors of the adjacent angles forming a linear pair form a right angle.

Answer 1

Answer: (D)

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$\left(a\right)$ 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$\left(b\right)$ and $\left(c\right)$ 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,$\frac{{180}^{\circ }}{2}={90}^{\circ }$

Hence each angle should be ${90}^{\circ }$. And we know that ${90}^{\circ }$ is known as right angle .hence option$\left(d\right)$ is correct.