7 2 Exterior Angle Theorem 7 2 Exterior

7 -2: Exterior Angle Theorem

7 -2: Exterior Angle Theorem EXTERIOR ANGLE: An angle of a triangle that forms a linear pair with one of the angles of the triangle. Remote Interior Angle Exterior Angle REMOTE INTERIOR ANGLES: The angles that do not form a linear pair with the exterior angle.

7 -2: Exterior Angle Theorem Identify each exterior angle. Then, identify the remote interior angles Exterior Angle Remote Interior Angles 4 2 & 3 5 1 & 3 6 1 & 3 7 1 & 2 8 1 & 2 9 2 & 3 Note that each exterior angle at a vertex share the same interior angles

7 -2: Exterior Angle Theorem 7 -3 (EXTERIOR ANGLE THEOREM): The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles. 2 4 = 1 + 2 Discuss Proof 1 3 4

7 -2: Exterior Angle Theorem If m 2 = 38 and m 4 = 134, what is m 5? 4 = 2 + 5 134 = 38 + 5 96 = 5 If m 2 = x + 17, m 3 = 2 x, and m 6 = 101, find the value of x. 6 = 2 + 3 101 = x + 17 + 2 x 101 = 3 x + 17 84 = 3 x 28 = x

7 -2: Exterior Angle Theorem Your Turn What is 1 if m 3 = 46 and m 5 = 96? 142 If m 2 = 3 x, m 3 = x + 34, and m 6 = 98, find the value of x. Then, find m 3. x = 16 m 3 = 50

7 -2: Exterior Angle Theorem Two “common sense” theorems are derived from the Exterior Angle Theorem 7 -4: The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles. Theorem 7 -5: If a triangle has one right angle, then the other two angles must be acute.

7 -2: Exterior Angle Theorem Assignment Worksheet #7 -2