Question

An angle whose measure is greater than $0{}^\circ $ but less than $90{}^\circ $ is known as
[a] Obtuse angle
[b] Acute angle
[c] Right angle
[d] None of these

Answer 1

Hint: Recall the definitions of an acute angle, an obtuse angle, and a right angle. Using the definition find which angle has its measure between $0{}^\circ $ and $90{}^\circ $. Hence determine which of the options is correct.

Complete step by step answer:

Before solving the question, we need to understand the definitions of the various types of angles and their properties.
[1] Zero Angle: An angle whose measure is $0{}^\circ $ is known as zero angle. ABA is the angle whose measure is $0{}^\circ $.

[2] Acute Angle: An angle whose measure is between $0{}^\circ $ and $90{}^\circ $ is known as acute angle. $\angle ABC$ is an acute angle shown below.

[3] Right Angle: An angle whose measure is $90{}^\circ $ is known as right angle. $\angle ABC$ shown below is a right angle.

[4] Obtuse angle: An angle whose measure is between $90{}^\circ $ and $180{}^\circ $ is called an obtuse angle. $\angle ABC$ shown below is a obtuse angle.

[5] Straight angle: An angle whose measure is $180{}^\circ $ is called a right angle. $\angle ABC$ shown below is a straight angle.

[6] Reflex angle: An angle whose measure is between $180{}^\circ $ and $360{}^\circ $ is known as reflex angle. $\angle ABC$ shown below is a Reflex angle

[7] Complete angle: An angle whose measure is $360{}^\circ $ is known as a complete angle. $\angle ABC$ shown below is a Complete angle.

Hence according to the definition, an angle whose measure is greater than $0{}^\circ $ and less than $90{}^\circ $ is an acute angle.
Hence option [b] is correct.

Note:
[1] The classification of angles on the basis of their measure is very important and is used to classify triangles into acute triangles, right triangles and obtuse triangles. It is used to relate various systems of measurement with each other.