Question

In the given figure $A,B,C,D$ are the concyclic points. The value of $x$ is

• A. ${50}^o$
• B. ${60}^o$
• C. ${70}^o$
• D. ${90}^o$

Answer 1

The correct option is A ${50}^o$

Sum of opposite angles of a cyclic quadrilateral = ${180}^0$.

In cyclic quadrilateral $ABCD$:

$\Rightarrow \angle BAD+\angle ADC={180}^0\Rightarrow {50}^0+\angle ADC={180}^0\Rightarrow \angle ADC={180}^0\Rightarrow \angle ADC+\angle CDE={180}^0(\because Sumofanglesonastraightline={180}^0.)\Rightarrow {130}^0+\angle CDE={180}^0\Rightarrow \angle CDE=x={50}^0$