Question

pls. answer fast. ........​

Answer 1

$\mathfrak{ANSWER:-}$

Since TN is a tangent to the circle,

∠OTN = 90°

Using Angle Sum Property in ΔONT we get,

∠ONT +∠NOT +∠OTN = 180

30 + ∠NOT + 90 = 180

120 +∠NOT = 180

∠NOT = 60

                                                                     

Now,

∠AOB + ∠NOT = 180° (Linear Pair)

∠AOB + 60 = 180

∠AOB = 120°

Now,

∠OAB = ∠OBA {Angle opposite to equal sides are equal (OA = OB)}

=> ∠OBA = x

Using Angle Sum Property in ΔOAB

∠OAB + ∠OBA +∠AOB = 180°

x + x + 120 = 180

2x = 60

x = 30°

                                                     

$\huge{\boxed{x=30}}$