Discussion
D is a point on side AB of a ΔABC such that CD is the bisector of ∠ACB. If ∠A = 50° and ∠B = 70°, then ∠ADC is equal to :
Answer: D
∠ADC is 100°.
\[ \begin{aligned} \angle C &= 180 - 50 - 70 = 60 \\ \angle ACD &= 60 / 2 = 30 \\ \angle ADC &= 180 - 50 - 30 = 100 \end{aligned} \]
In triangle ADC the angles at A and C are 50° and 30°, so the third is 100°. 30° is ∠ACD itself, and 70° and 50° are the given angles, not ∠ADC.
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