MCQ
In Fig. what is $y$ in terms of $x?$
- ✓$\frac{3}{2}\text{x}^\circ$
- B$\frac{4}{3}\text{x}^\circ$
- C$\text{x}^\circ$
- D$\frac{3}{4}\text{x}^\circ$
✓
Answer
Correct option: A.
$\frac{3}{2}\text{x}^\circ$
From figure,
$\angle\text{DOC}=180^\circ-\angle\text{AOD}$ (Both are Supplementary)
$\Rightarrow\angle\text{DOC}=180^\circ-3\text{y}^\circ$
Also, $\angle\text{ACB}=180^\circ-\angle\text{A}-\angle\text{B}$
$\Rightarrow\angle\text{ACB}=180^\circ-\text{x}^\circ-2\text{x}^\circ=180^\circ-3\text{x}^\circ$
And $\angle\text{ACD}=180^\circ-\angle\text{ACB}$
$=180^\circ-(180^\circ-3\text{x}^\circ)$
$\Rightarrow\angle\text{ACD}=3\text{x}^\circ$
Now, in $\triangle\text{OCD}$
$\angle\text{DOC}+\angle\text{OCD}+\angle\text{D}=180^\circ$
$180^\circ-3\text{y}^\circ+3\text{x}^\circ+\text{y}^\circ=180^\circ$ $\big[\angle\text{OCD}=\angle\text{ACD}\big]$
$\Rightarrow2\text{y}^\circ=3\text{x}^\circ$
$\Rightarrow\text{y}=\frac{3}{2}\text{x}^\circ$
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