Question

Which is the greatest angle in the given sets: \[\dfrac{1}{3}\] of a complete angle; \[\dfrac{1}{3}\] of a straight angle; or a right angle?

Answer 1

Hint:- Let us first know about Straight Angle, Complete Angle and Right Angle.
STRAIGHT ANGLE: An angle whose measure is exactly 180° is called a straight angle. It looks like a straight line.

COMPLETE ANGLE: An angle whose measure is 360° is called a complete angle.

RIGHT ANGLE: An angle whose measure is exactly 90° is called a right angle. It looks like the letter L.

Complete step-by-step answer:
Now, we know about Complete, Straight and Right angles.
\[\dfrac{1}{3}\] of a Complete Angle = \[\dfrac{1}{3}\] of 360°
\[\dfrac{1}{3}\] of a Straight Angle = \[\dfrac{1}{3}\] of 180°
Right Angle = 90°
\[\dfrac{1}{3}\]of 360 = \[\dfrac{1}{3}\times {{360}^{\circ }}\] = 120°
\[\dfrac{1}{3}\] of 180 = \[\dfrac{1}{3}\times {{180}^{\circ }}\] = 60°
Right Angle = 90°
We can see that 120° is the greatest angle in the given sets.
Therefore, the greatest angle in the given sets is \[\dfrac{1}{3}\] of a complete angle, because, \[\dfrac{1}{3}\] of a complete angle = 120°.

Note:- Let us know about Acute, Obtuse and Reflex angles.
ACUTE ANGLE: An acute angle is an angle whose measure is between 0° and 90°.

OBTUSE ANGLE: Obtuse angles are those angles whose measure is more than 90° but less than 180°.

REFLEX ANGLE: A reflex angle is the angle whose measure is more than 180° but less than 360°.