L is the incentre of ΔONP. If ∠OLP + ∠ONP = 195 degree, then what will be the value of ∠OLP?
Answer & explanation
Correct answer: option 4
\(\angle\)OLP + \(\angle\)ONP = 195
\(\angle\)OLP = 195 - \(\angle\)ONP
L is the incenter.
\(\angle\)OLP = 90 + \(\angle\)ONP/2
195 - \(\angle\)ONP = 90 + \(\angle\)ONP/2
105 = 3\(\angle\)ONP/2
\(\angle\)ONP = 70
\(\angle\)OLP = 195 - 70
\(\angle\)OLP = 125
Therefore, \(\angle\)OLP is \({125}^\circ\).