Lesson Page

Math A

Interior Angles of a Triangle

 

The sum of the interior angles of
any triangle is 180º.

 

 

This means that in triangle MNP to the left,    

   m<M + m<N + m<P = 180º.

 

The sum of the angles of ANY type of triangle is 180º.

     

 

Examples

 

1. In ABC, m<A = 42º and m<C = 63º.  What is the measure of <B ?

Let x = m<B.
Add up all three angles and set
them  equal to 180º.
Solve for x.

 x + 42 + 63 = 180
x + 105 = 180
x = 75
So m<B = 75º

 

2. The angles of a triangle are in the ratio of 1:2:3.  Find the measure of the smallest angle of the triangle.

Let x = smallest angle
    2x = second angle
    3x = largest angle

Then:
x + 2x + 3x = 180
          6x = 180
            x = 30

So the smallest angle measures 30º

 

 

3. The vertex angle of an isosceles triangle measures 58º.  Find the measure of a base angle.

The base angles are the 2
congruent angles in an isosceles
triangle.  So,
               Let x = a base angle

 

 

Then
x + x + 58 = 180
   2x + 58 = 180
         2x = 122
          x = 61

So a base angle measures 61º.

 


   Murray