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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