An angle is formed by two rays with a common end point. The rays forming the angle are called the sides of the angle and the common end point is known as the vertex of the angle.

What is Angle

The sides of the angle are AB and AC.
The vertex is A.
How to name the angle?

We can name the angle
  • by its vertex ∠A.
  • Using a point on each side and the vertex,as ∠BAC or ∠CAB.
  • Using a number ∠1.
 


Degree is the unit used to represent an angle measure and it denoted by the symbol º. A full angle formed around a point measures 360º. The angle at point are classified based on their measures as follows:

Type 
 Degree measure
 1. Acute angle  0º < x < 90º
 2. Right angle   x = 90º
 3. Obtuse angle  90º < x < 180º
 4. Straight angle  x =180º
 5. Reflex angle  180º < x < 360º

Let us see few examples on each of the above mentioned type.

The measure of an acute angle is greater than 0º and less than 90º.
Using math, if x is the measure of an acute angle then 0º < x < 90º.

If the angle measure x + y = 90º, then y is said to be the complementary measure of the angle whose measure is x.

Thus the complementary angle of an acute angle is also an acute angle.

Solved Example

Question:
Acute Angle

In the above diagram, the two angles 1 and 2 are complementary angles. Find the measure of each angle.
Solution:
 
measure of 1 + measure of 2 = 90                                             Definition of complementary angles
x + 3 + 2x - 3 = 90
                 3x = 90                                                                      Combining the like terms
                   x = 30º.
Measure of angle 1 = 2x - 3 = 2(30) - 3 = 60 - 3 = 57º.
Measure of angle 2 = x + 3 = 30 + 3 = 33º.

As the sum of three angles in a triangle is 180º, a triangle has at least two acute angles.
A triangle with all the three angles as acute is called an acute angled triangle.
 

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