In the figure angle X=72° , angle XYZ=46° . If YO and ZO are bisectors of angle xyz and angle xzy respectively of triangle XYZ , find angle

Question

In the figure angle X=72° , angle XYZ=46° . If YO and ZO are bisectors of angle xyz and angle xzy respectively of triangle XYZ , find angle OYZ and angle YOZ​

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Remi 1 month 2021-08-20T03:24:34+00:00 1 Answer 0 views 0

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    2021-08-20T03:26:24+00:00

    Answer:

    In the figure angle X=72° , angle XYZ=46° . If YO and ZO are bisectors of angle xyz and angle xzy respectively of triangle XYZ , find angle OYZ and angle YOZ​

    Step-by-step explanation:

    In fig  YO and ZO are respectively the bisector , and bisector bisect the angle in two equal parts  so

    angle (OYZ) = 1/2 angle (XYZ)

      angle (OYZ) = 1/2 (46) = 23 DEGREE

    NOW IN TRIANGLE XYZ by angle sum property

    x+y+z =180

    72 +46 +z  =180

    z = 180 -118

    z = 62 degree

    now apply angle sum property in triangle OYZ

    angle (OYZ) + angle (OZY)+ angle (YOZ)= 180

    23 +31 + angle (YOZ)= 180

    ANGLE (YOZ)= 180-54

     =126 DEGREE

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