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<M + m<N + m<P = 180°.

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

Examples

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

So m<B = 75°

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

So the smallest angle measures 30°

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°.