Q. 24.4( 332 Votes )

In Fig. 6.40, <sp

Answer :

Given:  X = 62o, ∠ XYZ = 54o

YO and ZO are the bisectors of XYZ and XZY respectively.
To Find:  ∠ OZY and ∠ YOZ.


Now, according to the question,

X + XYZ + XZY = 180o         (Sum of the interior angles of a triangle = 180°)

62o + 54o + XZY = 180o

116o + XZY = 180o

XZY = 64o


Now,

As ZO is the bisector of   XZY

OZY = 1/2   XZY

OZY = 32o


And,

As YO is bisector of   XYZ

OYZ = 1/2 XYZ 

OYZ = 27o


Now,

OZY + OYZ + O = 180o (Sum of the interior angles of the triangle = 180°)

32o + 27o + O = 180o

59o + O = 180o

O = 121o

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