Question

Explaining a Relationship
Explain how the exterior angle relates to the interior angles.

A triangle has angles A, B, C. The exterior angle to angle C is angle D.

Answer 1

The exterior-angle theorem: the measure of an exterior angle of a triangle equals the sum of the measures of the two opposite (remote) interior angles.

Given triangle with interior angles A, B, C and exterior angle D at vertex with interior angle C:

1. Interior angles of a triangle sum to 180°:
A + B + C = 180°.

2. An exterior angle and its adjacent interior angle form a linear pair, so they sum to 180°:
D + C = 180°.

3. Subtract the second equation from the first (or equate the right-hand sides):
A + B + C = D + C ⇒ A + B = D.

So D = A + B. In particular D is larger than either A or B individually (since A, B > 0).