MCQ
In the given figure, $AOB$ is a straight line. If $\angle\text{AOC}=(3\text{x} +10)^\circ$ and $\angle\text{BOC}=(4\text{x}-26)^\circ,$ then $\angle\text{BOC}=?$
- A$96^\circ$
- ✓$86^\circ$
- C$76^\circ$
- D$106^\circ$
✓
Answer
Correct option: B.
$86^\circ$
Since $AOB$ is a straight line,
$\angle\text{AOC}+\angle\text{BOC}=180^\circ$
$\Rightarrow(3\text{x}+10)+(4\text{x}-26)=180^\circ$
$\Rightarrow7\text{x}-16=180^\circ$
$\Rightarrow7\text{x}=196$
$\Rightarrow\text{x}=28$
So, $\angle\text{BOC}=4 \text{x}-26=4(28)-26=86^\circ$
$\angle\text{AOC}+\angle\text{BOC}=180^\circ$
$\Rightarrow(3\text{x}+10)+(4\text{x}-26)=180^\circ$
$\Rightarrow7\text{x}-16=180^\circ$
$\Rightarrow7\text{x}=196$
$\Rightarrow\text{x}=28$
So, $\angle\text{BOC}=4 \text{x}-26=4(28)-26=86^\circ$
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