I want to know the best answer of the question from Lines and Angles chapter of class 9^{th} ncert math. The question from exercise 6.3of math. Give me the easy way for solving this question of 2

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# 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. Q.2

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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°