Measurement Of Angles – Formula

There are different aspects of geometry used in our day to day life; the measurement of an angle is done by a tool known as a protector. One complete revolution equals 360o, and each angle is divided into 360 discrete quantities. It is denoted by a degree symbol ” o ” . There are different angles like- acute angle, obtuse angle, reflex angle, etc. Angles are formed when two rays are joined at a single point, and the lower side is called the initial side, the top side is called the terminal side, and the angle is formed, denoted by ∠. The measurement of angles formula is mentioned in the article. 

Types of angles

Angles are of basically 7 types, which are explained below:

Zero angle-  0o

Acute angle- these angles lie between 0o to 90o.

Obtuse angle- these angles are formed between 900 to 1800.

Right angle- this angle is exactly equal to 900.

Straight angle- this angle is also exactly equal to 1800.

Reflex angle- this angle is smaller than 3600, and it is greater than 180o.

Wide-angle- this angle has a complete rotation of 3600.

Critical angle formula

This angle refers to the incidence angle. Beyond this angle, there is a total reflection of the angle; this is derived from the normal trajectory, and the ray of the light strikes the medium lower refractive index, which is derived. This angle is greater than the incidence angle, known as internal reflection.

The critical angle is equal to the inverse function of sin, which is the refraction index per incidence index, and the formula for the critical angle is being given below:

 crit = sin-1 (n1/n2)

Here,

crit = critical angle

N1 = index of refraction.

N2 = index of incident.

Area of a right-angle triangle formula

A triangle that subtends an angle of exactly 90 degrees is denoted as the right-angle triangle; in a right-angle triangle, the side opposite to the angle is known as hypospadias, and the bottom side is known as the base; the left side is known as height. The formula to find right angle triangle is –

Area of a right-angle triangle = ½ x base x height

There is another way to find the area of a right-angle triangle, as we already know a rectangle subtends a 90-degree angle in each site. If we draw a diagonal from any side and divide the rectangle into two triangles, we will observe that we will get to right-angle triangles. We already know the rectangle area is equal to length into breadth.

                                        Area of a rectangle= L x B

If we divide the rectangle into two right-angled triangles and find the area of 2 sides, we will have to divide it by half, and we will get this.

 Area of a triangle = ½ x length x breadth

Trigonometric identities

Trigonometry identities are applied in a right-angle triangle, and with the help of this mathematical branch, we can easily find, the length of any side there are certain values of trigonometry identities which are given below:-

●      Sin

●      Cos

●      Tan

●      Cosec

●      Sec

●      Cot

Properties of an angle

Various kinds of angles exist, and in this section, we will discuss some of them and their properties as follows:

Linear pair: if there are two angles present and they form a linear pair, they are called to be the supplementary angle.

Vertical angles: if there are two angles and they are vertical angles, they are congruent.

Sum of triangle angle: the sum of all the interior angles of a triangle equals 180 degrees.

Exterior angles: An exterior triangle angle equals the sum of two adjacent interior angles.

Corresponding angles: this angle is formed when alignment crosses the same relative position of the intersection, and these corresponding angles are equal.

Vertically opposite angles: if two angles are present and vertically opposite to each other, then the angles will be equal to each other.

Laws of an angle

Below given are some of the laws of an angle we should strictly follow:

●      In a triangle, the sum of all angles is 180 degrees.

●      An angle of a quadrilateral has a sum of 360 degrees.

●      The angle of a straight line is 180 degrees.

●      There are 360 degrees of angle around a point or circle.

●      Vertically opposite angles are always equal.

●      Alternate angles are also equal.

●      Co interior angles are equal to 180 degrees.

Conclusion

We can use a tool name protector to measure any angle and angles are used in our day to day life. It belongs to a branch called geometry altogether; there are seven types of angles: right angle, obtuse angle, acute angle, reflex angle, etc.; in the above-written article, we have discussed every variety of angles. We have even discussed their properties and laws, an angle made up of booty is joined in a point, and the lower side is known as the initial side, and the upper side is known as the terminal side.