Exterior Angle Theorem

A triangle's exterior angle d:

equals the angles a plus b

and

is greater than angle a
is greater than angle b

Example:

exterior angle theorem 35+62=97

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 and d also add to 180°:

exterior angle theorem triangle a+b+c=180, c+d=180

The interior angles of a triangle add to 180°:a + b + c = 180°Angles c and d make a straight angle (180°):d + c = 180°So d + c equals a + b + c:d + c = a + b + cSubtract c from both sides:d = a + b

Works For Any Triangle's Exterior Angle

Example:

exterior angle theorem 27 and 40 inside triangle, 67 outside

The exterior angle is 40° + 27° = 67°

And 67° > 40°
And 67° > 27°

Example: How big is angle d?

exterior angle theorem 61 inside triangle, d outside

We can't calculate exactly, but we can say:

d° > 61°