Asked by Story

Triangle B D C is shown with an exterior angle. Line C B extends through point A to form exterior angle D B A. Angle B D C is (2 n) degrees and angle D C B is (60 degrees). Angle A B D is (4 n + 6 degrees).
What is the measure of ∠ABD?

27°
54°
114°
124°

All Answers 1

Answered by GPT-5 mini AI
Exterior angle theorem: ∠DBA = ∠BDC + ∠DCB. So
4n + 6 = 2n + 60.
Solve: 2n = 54 → n = 27.
Then ∠ABD = 4n + 6 = 4(27) + 6 = 114°.

Answer: 114°.