Question

How many angles in the given figure are less than a right angle?

(A) $2$
(B) $3$
(C)$4$
(D) $5$

Answer 1

Hint: In order to calculate the number of angles less than a right angle, we must firstly notice the numbers of angles created in the figure which is equal to a total of twenty angles. All are inside the figure and other angles outside the figure are greater than ${{90}^{\circ }}$. Clearly the angles which are ${{90}^{\circ }}$, the arms are perpendicular to each other. So, the angles greater than ${{90}^{\circ }}$ are more than perpendicular arms.

Complete step by step solution:
First of all, we should know what the right angle is? Right angle is an angle which measures exactly ${{90}^{\circ }}$.
It can be observed that all the angles outside the figure is more than ${{90}^{\circ }}$. So, they can’t be counted as per the requirement of the question.
When we observe inside the figure, it can be seen that the five angles at the inner corners of the figure is less than ${{90}^{\circ }}$ and the remaining five are more than ${{90}^{\circ }}$.
Thus, all the inner angles of the figure are less than right angles.
$5$ angles are less than a right angle.

Hence the correct answer is option (D).

Additional Information: The angle which is less than ${{90}^{\circ }}$ is called Acute angle. The angle which is ${{90}^{\circ }}$ exactly is called the Right angle. The angle which is greater than ${{90}^{\circ }}$ but less than ${{180}^{\circ }}$ is called Obtuse Angle. The angle which is ${{180}^{\circ }}$ exactly is called Straight Angle. The angle which is greater than ${{180}^{\circ }}$ is called Reflex Angle. The angle which is ${{360}^{\circ }}$ exactly is called Full Rotation.

Note: While solving this question, firstly, one should have the knowledge what a Right angle and angle smaller than it is called Acute angle. For further more information about the different types of angles, read the additional information provided above. In right angles, the arms are perpendicular to each other. So the obtuse angles have more extended angles than right angles.