MCQ
In Fig the value of $x$ is
:
:
- A$65^\circ$
- B$80^\circ$
- C$95^\circ$
- ✓$120^\circ$
✓
Answer
Correct option: D.
$120^\circ$
In $\triangle\text{ABD}$
$\angle\text{A}+\angle\text{B}+\angle\text{D}=180^\circ$
$\Rightarrow55^\circ+\angle\text{DBA}+25^\circ=180^\circ$
$\Rightarrow\angle\text{DBA}=180^\circ-55^\circ-25^\circ$
$=180^\circ-80^\circ$
$\Rightarrow\angle\text{DBA}=100^\circ$
So, $\angle\text{DBC}=180^\circ-\angle\text{DBA}$
$=180^\circ-100^\circ$
$\Rightarrow\angle\text{DBC}=80^\circ$
Now, in $\triangle\text{EBC}$
$\angle\text{E}+\angle\text{EBC}+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{E}+80^\circ+40^\circ=180^\circ$ $\big(\angle\text{DBC}=\angle\text{EBC}\big)$
$\Rightarrow\angle\text{E}=180^\circ-120^\circ=60^\circ$
Also, $\text{x}=180^\circ-\angle\text{E}=180^\circ-60^\circ$
$\Rightarrow\text{x}=120^\circ$
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