Question

In the given figure, $\angle ADC=$

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${75}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is D ${80}^{\circ }$

$In△ABC\angle BAC+\angle BCA+\angle ABC=180\left(Sumofthreeanglesoftraiangleis180\right)\angle BAC=60\left(Given\right)\angle BCA=20\left(Given\right)\Rightarrow 60+20+\angle ABC=180\Rightarrow \angle ABC=180-80=\mathrm{100....}\left(1\right)NowABCDisacyclicquadilateral\angle ABC+\angle ADC=180\Rightarrow \angle ADC=180-\angle ABC\Rightarrow \angle ADC=180-100\left[From\right(1\left)\right]\Rightarrow \angle ADC=80HenceOption\left(D\right)isthecorrectanswer$