Answer :

**Given: ∠X = 62 ^{o}, ∠ XYZ = 54^{o}**

**YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively.To Find: ∠ OZY and ∠ YOZ.**

Now, according to the question,

∠X + ∠XYZ + ∠XZY = 180^{o} (Sum of the interior angles of a triangle = 180°)

62^{o} + 54^{o} + ∠XZY = 180^{o}

116^{o} + ∠XZY = 180^{o}

∠XZY = 64^{o}

Now,

As ZO is the bisector of ∠ XZY∠OZY = 1/2 ∠ XZY

∠OZY = 32^{o}

And,

As YO is bisector of ∠ XYZ∠OYZ = 1/2 ∠XYZ

∠OYZ = 27^{o}

Now,

∠OZY + ∠OYZ + ∠O = 180^{o} (Sum of the interior angles of the triangle = 180°)

32^{o} + 27^{o} + ∠O = 180^{o}

59^{o} + ∠O = 180^{o}

∠O = 121^{o}

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