In the figure, ∠x = 62^o, ∠XYZ =54^o. if YO and ZO are the bisectors of ∠XYZ and ∠XZY respectivel of ΔXYZ, then ∠YOZ is

121^o

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105^o

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100^o

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120^o

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Solution

The correct option is A
121^o

In ∆ XYZ

ÐYXZ + ÐXYZ + ÐYZX = 180^o (angle sum property)

ÐYZX = 64^o

Now, in ∆ YOZ

ÐYOZ + ÐOYZ + ÐYZO = 180^o (angle sum property)

ÐYOZ + 27^o + 32^o = 180^o (YO and ZO are bisectors)

ÐYOZ = 121^o

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