Question

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

Answer 1

In quadrilateral ABCD,
$\therefore \angle ABC+\angle BCD+\angle CDA+\angle DAB={360}^{\circ }{40}^{\circ }+{50}^{\circ }+\angle CDA+{70}^{\circ }={360}^{\circ }\Rightarrow \angle CDA+{160}^{\circ }={360}^{\circ }\Rightarrow \angle CDA={360}^{\circ }-{160}^{\circ }={200}^{\circ }$

Now,$\angle CDA+\angle ADC={360}^{\circ }(\because$ Angle at a point)
${200}^{\circ }+x={360}^{\circ }$
$x={360}^{\circ }-{200}^{\circ }$

$x={160}^{\circ }$