Question

In the given diagram, find the value of x in degrees.

Answer 1

In quadrilateral ABCD,
$\therefore \angle ABC+\angle BCD+\angle CDA+\angle DAB={360}^{\circ }\left(1mark\right){40}^{\circ }+{50}^{\circ }+\angle CDA+{70}^{\circ }={360}^{\circ }\Rightarrow \angle CDA+{160}^{\circ }={360}^{\circ }\Rightarrow \angle CDA={360}^{\circ }-{160}^{\circ }={200}^{\circ }$ (0.5 mark)
Now,$\angle CDA+\angle ADC={360}^{\circ }(\because$ Angles at a point)
${200}^{\circ }+x={360}^{\circ }\Rightarrow x={360}^{\circ }-{200}^{\circ }\Rightarrow x={160}^{\circ }$
(1.5 mark)