Question

Classify the angles whose magnitude are given below: ${{128}^{\circ }}$

Answer 1

Hint: Classification of angle is done on the basis of acute, obtuse, reflex and complete angle. Means whether the angle is an obtuse angle or acute angle or reflex and so on. It depends on the magnitude of angle, where it lies. If it lies between ${{0}^{\circ }}$ and ${{90}^{\circ }}$ then it is known as acute angle, because of the acute shape of angle. If it lies between ${{90}^{\circ }}$ to ${{180}^{\circ }}$ it is known as an obtuse angle. Because of the obtuse shape of angle. If it lies between ${{180}^{\circ }}$and more known as reflex angle and so on.

Complete step-by-step solution:
So to find out or classify the angle by its magnitude we just only need to find the magnitude in which it lies, i.e. it can be in the interval of acute angle of ${{0}^{\circ }}$ to ${{90}^{\circ }}$or in the interval of obtuse angle of ${{90}^{\circ }}$ to ${{180}^{\circ }}$or in the interval of reflex angle of ${{180}^{\circ }}$ to ${{360}^{\circ }}$ or the perfect whole angle i.e. ${{360}^{\circ }}$.
So going by our question, asked about ${{128}^{\circ }}$,
As we can easily say that ${{128}^{\circ }}$ lies in the interval of ${{90}^{\circ }}$ to ${{180}^{\circ }}$ so it is an obtuse angle.
Hence ${{128}^{\circ }}$ is an obtuse angle.

Note: As I had clearly mentioned about the angle between the intervals, but if the angle comes out to be ${{0}^{\circ }}$,${{90}^{\circ }}$,${{180}^{\circ }}$, or ${{360}^{\circ }}$ than the condition will change. As when the angle is said to be ${{0}^{\circ }}$ or ${{180}^{\circ }}$ then it is known as a straight angle. And ${{90}^{\circ }}$ is known as the right angle.