1. Exterior Angles in a Triangle

2. 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.

3. 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

4. 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

5. Exterior Angle Theorem
∠ 1 = ∠ A + ∠ B

6. 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 °
x – 5 = 70°
x = 75°
∠ JKM = 2x - 5
∠ JKM = 2(75) - 5
∠ JKM =
∠ JKM = 145°

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

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

9. 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

10. 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°

11. 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°

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