Difference Between Obtuse and Acute Angle for JEE Main 2024

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Difference Between Obtuse And Acute Angle

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What is Obtuse and Acute Angle: Introduction

To differentiate between obtuse and acute angles: Angles play a fundamental role in understanding the relationships between lines, shapes, and objects. Two important classifications of angles are obtuse and acute angles. An obtuse angle is any angle that measures greater than 90 degrees but less than 180 degrees. It appears wider and more open than at a right angle (90 degrees). On the other hand, an acute angle is any angle that measures less than 90 degrees. It appears narrower and more compact compared to a right angle. Obtuse and acute angles can be found in various geometric configurations, such as triangles, quadrilaterals, and polygons, and their measurements and properties provide insights into the characteristics and properties of these shapes. Let’s understand them further in detail.

Category:	JEE Main Difference Between
Content-Type:	Text, Images, Videos and PDF
Exam:	JEE Main
Topic Name:	Difference Between Obtuse and Acute Angle
Academic Session:	2024
Medium:	English Medium
Subject:	Mathematics
Available Material:	Chapter-wise Difference Between Topics

Defining Obtuse Angle?

An obtuse angle is a type of angle in geometry that measures greater than 90 degrees but less than 180 degrees. It appears wider and more open than a right angle (90 degrees) but falls short of forming a straight line (180 degrees). In an obtuse angle, one of the rays extends beyond the perpendicular position, creating an angle that is larger than a right angle. The vertex of an obtuse angle is always located between the two rays. Obtuse angles are commonly encountered in various geometric shapes and can provide valuable insights into the relationships and properties of angles, lines, and polygons. The features of obtuse angles are:

Measurement: An obtuse angle measures greater than 90 degrees but less than 180 degrees.
Ray Extension: One of the rays of an obtuse angle extends beyond the perpendicular position, forming an angle that is larger than a right angle.
Vertex Position: The vertex of an obtuse angle is always located between the two rays.
Shape: An obtuse angle appears wider and more open compared to a right angle (90 degrees) but falls short of forming a straight line (180 degrees).
Relationship to Right Angle: An obtuse angle is larger than a right angle but smaller than a straight angle.
Naming: In geometric notation, an obtuse angle is often denoted using three points, with the vertex as the middle point, such as ∠ABC.
Angle Relationships: Obtuse angles can interact with other angles, forming complementary angles (when combined with another angle to form a right angle) or supplementary angles (when combined with another angle to form a straight angle).

Defining Acute Angle?

An acute angle is a type of angle in mathematics that measures less than 90 degrees. It appears narrower and more compact compared to a right angle (90 degrees). In an acute angle, both rays originate from the same endpoint and form a sharp V-shape. The vertex of an acute angle is located between the two rays. Acute angles are commonly found in geometric shapes, such as triangles, where all interior angles are acute. Understanding acute angles is essential for analyzing the properties and relationships of angles, lines, and polygons in geometry. The features of acute angles are:

Measurement: An acute angle measures less than 90 degrees.
Ray Configuration: The two rays of an acute angle originate from the same endpoint, forming a sharp V-shape.
Vertex Position: The vertex of an acute angle is located between the two rays.
Shape: An acute angle appears narrower and more compact compared to a right angle (90 degrees).
Relationship to Right Angle: An acute angle is smaller than a right angle but larger than a zero angle (a straight line).
Naming: In geometric notation, an acute angle is often denoted using three points, with the vertex as the middle point, such as ∠ABC.
Angle Relationships: Acute angles can interact with other angles, forming complementary angles (when combined with another angle to form a right angle) or supplementary angles (when combined with another angle to form a straight angle).

Obtuse and Acute Angle Differences

S.No	Category	Obtuse Angle	Acute Angle
1.	Measurement	Greater than 90 degrees but less than 180 degrees	Less than 90 degrees
2.	Ray Configuration	One ray extends beyond the perpendicular position	Rays form a sharp V-shape from the same endpoint
3.	Properties	Provides insights into the properties of angles and shapes	Helps analyze the characteristics and relationships of angles and polygons
4.	Shape	Wider and more open compared to a right angle	Narrower and more compact compared to a right angle
5.	Relationship to Right Angle	Larger than a right angle	Smaller than a right angle
6.	Angle Relationships	Can form supplementary angles with other angles	Can form complementary angles with other angles

These differences highlight how obtuse and acute angles have distinct measurements, configurations, and effects on angle relationships and geometric properties.

Summary

Obtuse and acute angles are two types of angles in geometry. Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They appear wider and more open than at a right angle. Examples include angles in triangles where one angle is greater than 90 degrees. Whereas, Acute angles are angles that measure less than 90 degrees. They appear narrower and more compact compared to a right angle. Examples include angles in equilateral triangles and angles formed by the hands of a clock when indicating specific times. Both obtuse and acute angles are fundamental concepts in geometry, and their measurements and properties play significant roles in understanding shapes, angles, and relationships.

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.