Question
Calculate the value of x in the given figure.
✓
Answer
Produce CD to cut AB at E. 
Now, in $\triangle\text{BDE},$ we have, Exterior $\angle\text{"CDB}=\angle\text{CEB}+\angle\text{DBE}$$\Rightarrow\text{x}^\circ=\angle\text{CEB}+45^\circ\ ....(\text{i)}$
In $\triangle\text{AEC}$ we have, Exterior $\angle\text{CEB}=\angle\text{CAB}+\angle\text{ACE}$$55^\circ+30^\circ=85^\circ$
Putting $\angle\text{CEB}=85^\circ$ in (i), we get,$\text{x}^\circ=85^\circ+45^\circ=130^\circ$
$\therefore\text{x}=130$
Now, in $\triangle\text{BDE},$ we have, Exterior $\angle\text{"CDB}=\angle\text{CEB}+\angle\text{DBE}$$\Rightarrow\text{x}^\circ=\angle\text{CEB}+45^\circ\ ....(\text{i)}$In $\triangle\text{AEC}$ we have, Exterior $\angle\text{CEB}=\angle\text{CAB}+\angle\text{ACE}$$55^\circ+30^\circ=85^\circ$
Putting $\angle\text{CEB}=85^\circ$ in (i), we get,$\text{x}^\circ=85^\circ+45^\circ=130^\circ$
$\therefore\text{x}=130$
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