In a triangle, the angle bisector of an angle divides the opposite side into segments that are proportional to the adjacent sides. Calculation:
Triangle Sum Property: The sum of the interior angles of a triangle is always 180∘. For triangle △ABC, we have: ⇒∠A+∠B+∠C=180∘ ⇒∠C=180∘−50∘−70∘ ⇒∠C=60∘ Angle Bisector Property: Since CD is the bisector of ∠ACB, it divides ∠C into two equal parts. Thus, ∠ACD=∠BCD=∠C∕2=60∘∕2=30∘ Angle Calculation at Point D: In △ADC, we need to find ∠ADC. The sum of angles in △ADC is also 180∘. ⇒∠A+∠ACD+∠ADC=180∘ Substitute the known values: 50∘+30∘+∠ADC=180∘ ⇒∠ADC=180∘−80∘=100∘