Calculate the value of x in the given figure.
Question:

Calculate the value of x in the given figure.

Solution:

Join A and D to produce AD to E.

Then,

$\angle C A D+\angle D A B=55^{\circ}$ and

$\angle C D E+\angle E D B=x^{\circ}$

Side AD of triangle ACD is produced to E.

$\therefore \angle C D E=\angle C A D+\angle A C D \quad \ldots(i)$ (Exterior angle property)

Side AD of triangle ABD is produced to E.

$\therefore \angle E D B=\angle D A B+\angle A B D \ldots(i i)$ (Exterior angle property)

Adding (i) and (ii) we get,

$\angle C D E+\angle E D B=\angle C A D+\angle A C D+\angle D A B+\angle A B D$

$\Rightarrow x^{\circ}=(\angle C A D+\angle D A B)+30^{\circ}+45^{\circ}$

$\Rightarrow x^{\circ}=55^{\circ}+30^{\circ}+45^{\circ}$

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

$\Rightarrow x=130$