Question

The diagram shows △ABC and BD (just imagine there's a right arrow above the BD).
What is the measure of ∠ACD?

Answer 1

I don't have the diagram, so I need one clarification before I can give a numeric answer: does the arrow over BD mean BD is a ray with endpoint B going through D (i.e. ray BD)? And where is point D located relative to triangle ABC (on which side or extension)?

If you can upload the picture or describe the configuration and any given angle measures/marks, I can solve it exactly.

Meanwhile, here are the common cases and the formulas you can use once you tell me where D is:

- If D lies on the extension of BC beyond C (so CD is the extension of BC), then ∠ACD is an exterior angle at C and equals the sum of the two remote interior angles:
∠ACD = ∠A + ∠B.

- If D lies on AC (so D is between A and C), then ∠ACD is the angle formed by AC and CD along the same line and equals 0° (degenerate) or you'd instead be interested in ∠BCD or ∠ADC — specify which.

- If D lies on the extension of BA beyond A (i.e. BD is a ray in some other direction), describe the picture or give angle measures and I will compute ∠ACD using the triangle angle-sum or exterior-angle theorems.

Send the diagram or the missing angle values/locations and I’ll finish the solution.