Interior Angles of a Triangles Topic Index | Geometry Index | Regents Exam Prep Center

 Theorem: The sum of the measures of the interior angles of any triangle is 180°.

 In at the left,   m

 Remember that this theorem works for ANY type of triangle.  The sum of the angles in ANY type of triangle is 180°.

 Examples

 1 In ABC, m

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

 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 30°

 3 The vertex angle of an isosceles triangle measures 58°  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 61°.

 Topic Index | Geometry Index | Regents Exam Prep Center Created by Michael Murray