Question

In the figure, computer the value of x,

Answer 1

In the figure,

$\angle ABC={45}^{\circ },\angle BAD={35}^{\circ }$ and $\angle BCD={50}^{\circ }$

Join BD and produce it E

In $\Delta ABD$,

Ext. $\angle 1=\angle A+\angle 3$ .....(I)

and in $\Delta CBD$,

Ext.$\angle 2=\angle C+\angle 4$ ....(ii)

Adding we get

$\angle 1+\angle 2=\angle A+\angle 3+\angle C+\angle 4$

$\Rightarrow x=\angle A+\angle 3+\angle 4+\angle c$

$\Rightarrow x=\angle A+\angle B+\angle C$

$\Rightarrow x={35}^{\circ }+{45}^{\circ }+{50}^{\circ }={130}^{\circ }$

$\therefore x={130}^{\circ }$