Question

If angle A = 120°, what is angle B? Explain. If angle D = 40°, what is angle E? Is your reasoning the same? If the sum of angle B, angle C, and angle D is 180°, what is angle C?

Answer 1

Angle A and B are supplementary: both form a 180° angle.

So, if A=120° , then B=180°-120°=60°.

Angle D and E are also supplementary and form a 180° angle.

If D=40°, then E=180°-40°=140°.

The reasoning is the same that for the previous pair of angles.

The sum of the interior angles of a triangle is equal to 180°, so we can write:

`\begin{gathered} B+C+D=180\degree \\ C=180\degree-B-D \\ C=180\degree-60\degree-40\degree \\ C=80\degree \end{gathered}`

Answer:

B=60°

E=140°

C=80°