MCQ
In $\triangle\text{RST}$ what is the value of $x?$
- A$40^\circ$
- B$90^\circ$
- C$80^\circ$
- ✓$100^\circ$
✓
Answer
Correct option: D.
$100^\circ$
In $\triangle\text{RST}$
$\angle\text{R}+\angle\text{S}+\angle\text{T}=180^\circ$
$\Rightarrow2\text{a}^\circ+\text{x}^\circ+2\text{b}^\circ=180^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-2(\text{a}+\text{b})^\circ\dots(1)$
Now in $\triangle\text{ROT}$
$\angle\text{ORT}+\angle\text{ROT}+\angle\text{OTR}=180^\circ$
$\Rightarrow\text{a}^\circ+140^\circ+\text{b}^\circ=180^\circ$
$\Rightarrow(\text{a}+\text{b})^\circ=180^\circ-140^\circ=40^\circ\dots(2)$
From $(1)$ and $(2)$
$\text{x}^\circ=180^\circ-2(40^\circ)$
$\Rightarrow\text{x}=100^\circ$
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