Introduction to three angles of a triangle:

Three angles of a triangle article deals with the properties of the three angles of a triangle and the model problems related to it

 

Definition of three angles of a triangle:

The triangle is a two-dimnesional shape with three angles. These three angles are said to be interior angles of the triangle and it will sum up to 180 degrees. These three angles are classified into three types:

They are

  1. Right angle
  2. acute angle
  3. obtuse angle

Angle 1+angle 2+ angles 3= 180 degrees.

 

Three types of angles:

 

Right angle:

Right angle measures exactly 90 degrees.

Acute angle:

Acute angle measures less than 90 degrees.

Obtuse angle:

Obtuse angle measures greater than 90 degrees.

Depending on the angles, the triangles are calssified as right triangle, acute triangle and obtuse triangle respectively.        

                                                                    types of angles       

 

Model problems to three angles in a triangle

 

Example 1: find the angle in the right triangle when one of the angles is 60 degrees?

Solution:

Since it is a right triangle, one angle is 90 and another angle is 60

We know that

Sum of three angles = 180

90+60+x= 180
150+x= 180

x= 180-150

x= 30 degrees

Therefore, the third angle in the right triangle is 30 degrees.

Example 2:

Find the unknown angle of the triangle when first two angles are 98 degrees and   45 degrees

Solution:

Since one of the angles is greater than 90 degrees, it is an obtuse triangle

Here two angle are given

We know that

Sum of the three angles= 180

98+45+x= 180

143+x= 180

x=180-143

x= 37 degrees

Therefore, the third angle in the obtuse triangle is 37 degrees

 

Example: 3 Find the unknown angle in the triangle when first two angles are 65 and 55 degrees

Solution:

Here two angles of the triangle are given that is 70 and 55 degrees.

We know that

Sum of the three angles= 180

70+55+x= 180

125+x= 180

x=180-125
x= 55 degrees

 The third angle of the triangle is 55 degrees.

Here all angles in the triangle is less than 90 degrees, so this triangle is an acute triangle

Note: angles in triangle determines whether it is an acute or obtuse or right triangle