In the given figure, ∠ ONY = 50° and ∠ OMY = 15°. Then the value of the ∠ MON is

Let , MY and ON intersect at point Z.
As, OM = OY , their opposite angles must be equal .∠OMY = ∠OYM = 15. Hence, ∠MOY = 180 - 15 - 15 = 150.
Also , ON = OY , their opposite angles must be equal. ∠ONY = ∠OYN = 50. Hence, ∠ZYN= ∠OYN-∠ONM = 50-15= 35.
So, ∠NZY= 180-50-35 = 95.
So, ∠OZY = 180-95 = 85
So, ∠ZOY= 180 - 85 - 15 = 80.
As we already got that , ∠MOY = 150 , now ∠MON = ∠MOY - ∠ZOT = 150 - 80 = 70.