1. 4-2 Angles of Triangles Objectives: The student will be able to: 1. Apply the Triangle-Sum Theorem. 2. Apply the Exterior Angle Theorem.

2. Angle Sum Theorem – the sum of the measures of the angles of a triangle is 180°. Third Angle Theorem – If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Exterior Angle – formed by one side of the triangle and the extension of another side. Angle 1 is an exterior angle of ΔABC. Remote Interior Angle – The interior angles of the triangle not adjacent to a given exterior angle. Angle 2 & Angle 3 are remote Interior angles.

3. Exterior Angle Theorem – The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 80 + 60 = 140° Example 1: Find the value of x. Exterior Angle =The two remote interior angles 78 =55 + x -55 23 = x

4. Example 2: Find the. Exterior Angle =The two remote interior angles 145 =95 + 2x -95 50 = 2x 25 = x 50

5. Example 3: Find the. Example 4: Find the.