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In Figure, X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of Δ XYZ, find OZY and YOZ.
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10/07/2021 12:28 pm
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In Figure, X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of Δ XYZ, find OZY and YOZ.
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10/07/2021 12:35 pm
We know that the sum of the interior angles of the triangle.
X + XYZ + XZY = 180°
Putting the values as given in the question we get,
62° + 54° + XZY = 180°
XZY = 64°
Now, we know that ZO is the bisector so,
OZY = 1/2 XZY
∴ OZY = 32°
Similarly, YO is a bisector and so,
OYZ = 1/2 XYZ
Or, OYZ = 27° (As XYZ = 54°)
Now, as the sum of the interior angles of the triangle,
OZY + OYZ + O = 180°
Putting their respective values, we get,
O = 180°  32°  27°
Hence, O = 121°
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