## What is Obtuse and Acute Angle: Introduction

## FAQs on Difference Between Obtuse and Acute Angle for JEE Main 2024

1. Can an angle be both obtuse and acute?

No, an angle cannot be both obtuse and acute simultaneously. By definition, an obtuse angle measures greater than 90 degrees but less than 180 degrees, while an acute angle measures less than 90 degrees. These two types of angles have distinct measurement ranges and characteristics. An angle's classification as either obtuse or acute is determined solely by its measurement. It will either have a measurement greater than 90 degrees, making it obtuse, or a measurement less than 90 degrees, making it acute.

2. What shape does an obtuse angle resemble?

An obtuse angle resembles an "open" V-shape. It appears wider and more open compared to a right angle (90 degrees), but it falls short of forming a straight line (180 degrees). Visualizing an obtuse angle can be likened to opening your arms wider than shoulder-width apart, creating an angle that is larger than a right angle but still leaving a gap before reaching a straight line. The arms of the "V" extend outwards, indicating the openness of the angle.

3. Can acute angles be bisected?

Yes, acute angles can be bisected. Bisecting an angle means dividing it into two equal parts. For an acute angle, you can draw a line from the vertex of the angle that passes through the midpoint of the angle, creating two congruent acute angles. This process can be done using a compass and a straightedge. Bisecting acute angles is a common geometric construction that helps in various mathematical and geometrical applications.

4. Can obtuse angles be congruent?

Yes, obtuse angles can be congruent. Congruent angles have the same measurement, regardless of their type. Since an obtuse angle is defined as measuring greater than 90 degrees but less than 180 degrees, two obtuse angles can be congruent if they have the same measurement within that range. For example, two obtuse angles measuring 120 degrees each would be congruent. Congruence is a property that depends solely on the equality of angle measurements, and it applies to angles of any type, including obtuse angles.

5. Can acute angles be supplementary to each other?

No, acute angles cannot be supplementary to each other. Supplementary angles are a pair of angles that add up to 180 degrees. Since acute angles have measurements less than 90 degrees, the sum of two acute angles will always be less than 180 degrees. Therefore, two acute angles cannot be supplementary to each other. Supplementary angles are typically formed by a combination of an acute angle and an obtuse angle or two obtuse angles.