Angle is the base of geometry, it is impossible for anyone to understand geometry without learning about angles. Angle is formed at an intersection of two rays. An Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angle is not just the interception of plane rays, even curved rays intersection point can be measured via angle.
Angles and Types of Angles
Angle is one of the most important and perhaps the most basic chapters of geometry. Learning this chapter to the core and elaborately lets you understand the foundation of the subject. An angle constitutes two components, side, and the vertex. There are many ways of an intersection of sides to form a vertex. The following section throws light on the various types of angles in detail:
Types of Angles
1. Acute Angle
An angle which is less than 90 ° is known as an acute angle. Acute angle measures between 0 to 90 °. The following figure shows that when two sides A and B intersect at point O and form a vertex. The angle at which these rays intersects is less than 90° thus forms an acute angle.
2. Obtuse Angle
An angle which is greater than 90 ° is known as an obtuse angle. An obtuse angle measure between 90 ° to 180 °. An obtuse angle is an opposite angle of an acute angle. The following figure shows that point O where A and B intersects is greater than 90° and less than 180°, thus it is an obtuse angle.
3. Right Angle
The right angle is an angle which measures exactly 90 °and any angle less or greater than 90 °will not be considered as a right angle. The following figure illustrates that A and B intersect to form a 90 ° angle.
4. Straight Angle
An angle which measures 180 ° is known as a straight angle. This looks similar to a plane straight line and hence is named as a straight angle. The following figure will clear the concept.
5. Reflex Angle
An angle which measures greater than 180 degrees but less than 360 degrees is known as a reflex angle. A reflex angle is supposed to be a complementary angle for acute angle and is on the other side of the line. The following figure illustrates the reflex angle.
Geometry finds its basis in angles. From basic closed shapes to tricky trigonometry questions, angles form a part of each and every chapter. Understanding these surely helps in perfecting knowledge of geometry and trigonometry both.
Solved Example for You
Question 1: The figure shown below is of a straight angle, ∠AOB. Find the missing angle in the given figure:
Answer : ∠AOB is a straight angle, that is ∠AOB = 180°
∠AOB = ∠AOC +∠COB
180 = ?+55
? = 180-55
? = 125 °
The missing angle in the above figure: 125°
Question 2: What are the types of triangles with respect to the angles?
Answer: When we look at the different types of triangles on the basis of angles, they are of 5 types. They are Right Triangle, Obtuse Triangle, Acute Triangle, and Equiangular Triangle.
Question 3: What is an Equilateral Triangle?
Answer: An equilateral triangle is a kind of triangle which comprises of 3 equal sides and equal angles. Moreover, each side of this triangle is of the same length and every angle is going to be of the same measure which is 60°.
Question 4: Give the definition of a triangle.
Answer: A triangle is a three-sided polygon which is a close figure consisting of 3 lines that link at the endpoint to each other. The major properties of a triangle are that they are the sum of the interior angle of the triangle is going to be 180°. Similarly, the sum of the exterior angles is always going to be 360°. Further, we can classify triangles on the basis of their sides and interior angles.
Question 5: Define an obtuse triangle.
Answer: An obtuse triangle is one having two acute angles and one obtuse angle. You must know that an acute angle is ones which measure less than 90° while the obtuse angle one is one which measures over 90°. Thus, an obtuse triangle refers to a combination of 2 acute angles and 1 obtuse angle.