Question

In the given diagram, the value of x is ___ degrees.

Answer 1

In quadrilateral ABCD,
$\angle ABC+\angle BCD+\angle CDA+\angle DAB={360}^{\circ }{40}^{\circ }+{50}^{\circ }+\angle CDA+{70}^{\circ }={360}^{\circ }\Rightarrow \angle CDA+{160}^{\circ }={360}^{\circ }\Rightarrow \angle CDA={360}^{\circ }-{160}^{\circ }={200}^{\circ }$
Now,$\angle CDA+\angle ADC={360}^{\circ }(\because$ Angle at a point adds up to ${360}^{\circ }$
${200}^{\circ }+\angle ADC={360}^{\circ }\Rightarrow \angle ADC={360}^{\circ }-{200}^{\circ }\Rightarrow \angle ADC={160}^{\circ }$
Hence, the value of x is ${160}^{\circ }$