An Exterior Angle of a Triangle
An exterior of a triangle is created by extending one side of the triangle.
"Exterior" means outside and "Interior" means inside.
Examples:
Any exterior angle of a triangle is equal to the sum of the two interior opposite angles.
![Picture](/uploads/2/3/4/0/23408802/8072059.png)
1. Find the sizes of x and y in the triangle.
Solution
180 = 34 + 30 + y
= 64 + x
y = 180 - 64
= 116°
x = 180 - 116
= 64°
∴ y° = 116° and x° = 64°
*notice how x = 64° and 30 + 34 = 64°*
Solution
180 = 34 + 30 + y
= 64 + x
y = 180 - 64
= 116°
x = 180 - 116
= 64°
∴ y° = 116° and x° = 64°
*notice how x = 64° and 30 + 34 = 64°*
![Picture](/uploads/2/3/4/0/23408802/5574033.png)
2. Find the value of y in this triangle.
Solution
y° = 45° + 41°
y = 86°
∴ y = 86°
Solution
y° = 45° + 41°
y = 86°
∴ y = 86°
![Picture](/uploads/2/3/4/0/23408802/5144468.png)
3. Find the value of n in the triangle on the right.
Solution
116° = 45° + n°
n°= 116 - 45
n° = 71°
Solution
116° = 45° + n°
n°= 116 - 45
n° = 71°
Quiz
2. In the following triangles, find the size os each angle marked by a variable, and say whether it is an interior or an exterior angle.
2. Find the value of each variable: