Question : ${L}$ is the incentre of $\triangle ONP$. If $\angle {OLP}+\angle {ONP}=195^\circ$, then what will be the value of $\angle {OLP}$?
Option 1: $115^\circ$
Option 2: $140^\circ$
Option 3: $135^\circ$
Option 4: $125^\circ$
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Correct Answer: $125^\circ$
Solution :
Given: $\angle {OLP}+\angle {ONP}=195^\circ$
⇒ $\angle {OLP}=195^\circ-\angle {ONP}$
L is the incentre
So, $\angle OLP = 90^\circ+\frac{1}{2}\angle ONP$
⇒ $195^\circ-\angle {ONP} = 90^\circ+\frac{1}{2}\angle ONP$
⇒ $105^\circ= \frac{3}{2}\angle ONP$
⇒ $\angle ONP=70^\circ$
$\therefore \angle OLP = 195^\circ-70^\circ= 125^\circ$
Hence, the correct answer is $125^\circ$.
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