Question

Which one of the following statements is not false?

• A. If two angles forming a linear pair, then each of these angle is of measure $90°$.
• B. Angles forming a linear pair can both be acute angles.
• C. One of the angles forming a linear pair will be the obtuse angles.
• D. Bisectors of the adjacent angles forming a linear pair form a right angle.

Answer 1

The correct option is C

One of the angles forming a linear pair will be the obtuse angles.

Explanation for the correct option:

Option (C): One of the angles forming a linear pair will be an obtuse angle.

It is known that when two angles form linear pairs, they are supplementary. i.e., they add up to form $180$ degrees.

Thus, one angle has to be acute and the other has to be obtuse.

Hence, option (C) is the correct answer.

Explanation for the incorrect options:

Option (A): If two angles forming a linear pair, then each of these angle is of measure $90°$.

Each angle that forming a linear pair is of measure $90°$ only if they are equal.

Thus, the given statement is false.

Option (B): Angles forming a linear pair can both be acute angles.

It is known that An acute angle is the one that is smaller than the right angle.

So, angles forming a linear pair cannot both be acute angles.

Thus, the given statement is false.

Option (D): Bisectors of the adjacent angles forming a linear pair form a right angle.

It is known that the bisectors of the angles of a linear pair are at a right angle.

So, the bisectors of the adjacent angles forming a linear pair do not form a right angle.

Thus, the given statement is false.