2. In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δ XYZ, find ∠OZY and ∠YOZ.
Solution: We know that the sum of the interior angles of the triangle. So, ∠X +∠XYZ +∠XZY = 180° Putting the values as given in the question we get, 62°+54° +∠XZY = 180° Or, ∠XZY = 64° Now, we know that ZO is the bisector so, ∠OZY = ½ ∠XZY ∴ ∠OZY = 32° Similarly, YO is a bisector and so, ∠OYZ = ½ ∠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°
