Exterior Angles in a Triangle

Angles When the sides of a triangle 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 in measure to the sum of the measures of its two remote interior angles. remote interior angles Exterior angle

Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the interior opposite angles exterior angle remote interior angles 3 2 1 4 ∠ 1 + ∠ 2 = ∠ 4

Exterior Angle Theorem ∠ 1 = ∠ A + ∠ B

Examples Find ∠ JKM 2x – 5 = x + 70° x – 5 = 70° x = 75° Exterior angle = Sum of the interior opposite angles ∠ JKM = ∠ KJL + ∠ JLK 2x – 5 = x + 70° x – 5 = 70° x = 75° ∠ JKM = 2x - 5 ∠ JKM = 2(75) - 5 ∠ JKM = 150 - 5 ∠ JKM = 145°

Examples Exterior angle = Sum of the interior opposite angles ∠ JHF = ∠ HFG + ∠ FGH 111 = ∠ HFG + ∠ FGH 111 = 60 + ∠ FGH ∠ FGH = 111 – 60° ∠ FGH = 51°

x = 68° y = 112° Examples Find x & y 82° 30° x y To find y: Exterior angle = Sum of the interior opposite angles y = 30 + 82 y = 112˚ 82° 30° x y To find x: Sum of the angles in a triangle is 180˚ 180 = 30 + 82 + x 180 = 112 + x x = 68˚ x = 68° y = 112°

Examples Solve for y in the diagram. To find y: Exterior angle = Sum of the interior opposite angles 4y + 35 = 56 + y 4y – y = 56 – 35 3y = 21 Y= 21 ÷ 3 = 7

Examples Solve for x and y in the diagram. Solution: To find y: We know that vertical opposite angles are equal Therefore y = 67° To find x : Sum of angles in a triangle is 180° 67° + 45° + x = 180° 112° + x = 180° x = 180° - 112° = 68°

Examples Solve for x and y in the diagram. Solution: To find y: Sum of adjacent angles = 180° y + 130° = 180° y = 180° - 130° y = 50° To find x: Sum of adjacent angles = 180° x + 120° = 180° x = 180° - 120° x = 60°

TRY THESE 1. Find x 2. Find x and y