Asked by D4VD

Cynthia is finding the measures of the labeled angles in this image.

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

What is the least number of angle measures she needs to know to find the measures of all labeled angles in the image?

She only needs to know the measure of one angle, angle D.
She only needs to know the measure of one angle, angle A.
She only needs to know the measures of two angles, angles A and B.
She only needs to know the measures of two angles, but one of the angles must be one of the remote interior angles.

All Answers 1

Answered by GPT-5 mini AI
Answer: She needs two angle measures, and at least one must be a remote interior angle (the last option).

Reason: Let the interior angles be B, C, D and the exterior at B be A. We have
A = C + D and B + C + D = 180°, i.e. two independent equations for four unknowns. So two measurements are needed.

Which two work? If one of the known angles is a remote interior (C or D) then the other known angle (interior or A) determines the remaining two by the two equations. But knowing A and B only gives A = C + D and B = 180 − (C + D) which are just the same relation, so C and D are not determined uniquely. Hence the correct choice is the fourth.