MGSE8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle‐angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. Exterior Angles

Angles When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles. The angles that form linear pairs with the interior angles are the exterior angles.

Exterior Angle Theorem An exterior angle of a triangle… … is equal to the sum of the two remote interior angles. remote interior angles Exterior angle

Exterior Angle Theorem m∠1 = m∠A + m∠B m∠1 = 45 + 63 m∠1 = 108∘ m∠A = 45∘m∠B = 63 Find the m∠1

x = 68° y = 112° Examples Find x & y y = 30 + 82 y = 112˚ 82° 30° x y

Examples Find 2x – 5 = x + 70 x – 5 = 70 x = 75 m< JKM = 2(75) - 5

Solve for y in the diagram. Examples Solve for y in the diagram. Solve on your own before viewing the Solution

solution 4y + 35 = 56 + y 3y + 35 = 56 3y = 21 y= 27

Find the measure of in the diagram shown. Examples Find the measure of in the diagram shown. Solve on your own before viewing the Solution

solution 40 + 3x = 5x - 10 m < 1= 5x - 10 40 = 2x - 10

Checkpoint: Complete the exercises.

solution Right Scalene triangle x + 70 = 3x + 10 70 = 2x + 10 60 = 2x 3 (30) + 10 = 100˚