Question

In the given figure, ABCD is a cyclic quadrilateral. What is the value of $\frac{x^{\circ }}{{50}^{\circ }}$?

• A. $3^{\circ }$
• B. $4^{\circ }$
• C. ${50}^{\circ }$
• D. $2^{\circ }$

Answer 1

The correct option is D $2^{\circ }$

We have, $\angle CDA={180}^{\circ }-{80}^{\circ }={100}^{\circ }$
and, $\angle ABC+\angle x={180}^{\circ }$
$\angle ABC={180}^{\circ }-x^{\circ }$
Now, $\angle CDA+\angle ABC={180}^{\circ }$ [sum of opposite angles in a quadrilateral is ${180}^{\circ }$]
$\Rightarrow {100}^{\circ }+({180}^{\circ }-x^{\circ })={180}^{\circ }\Rightarrow {280}^{\circ }-x^{\circ }={180}^{\circ }$
$\Rightarrow x^{\circ }={100}^{\circ }$
$\therefore \frac{x^{\circ }}{{50}^{\circ }}=\frac{{100}^{\circ }}{{50}^{\circ }}=2^{\circ }$