Exterior Angle Theorem
The exterior angle d of a triangle:
- equals the angles a plus b
- is greater than angle a, and
- is greater than angle b
Example:
The exterior angle is 35° + 62° = 97°
And 97° > 35°
And 97° > 62°
Why?
Because the interior angles of a triangle add to 180°, and angles c+d also add to 180°:
The interior angles of a triangle add to 180°:a + b + c = 180°
Angles c and d make a straight angle, which is 180°:d + c = 180°
So d + c equals a + b + c:d + c = a + b + c
Subtract c from both sides:d = a + b
Works For Any Triangle's Exterior Angle
Example:
The exterior angle is 40° + 27° = 67°
And 67° > 40°
And 67° > 27°
Example: How big is angle d?
We can't calculate exactly, but we can say:
d° > 61°