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Question

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


A

121o

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B

105o

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C

100o

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D

120o

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Solution

The correct option is A

121o


In ∆ XYZ

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

ÐYZX = 64o

Now, in ∆ YOZ

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

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

ÐYOZ = 121o


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