Question

X=62°,XYZ=54°. If YO and ZO are the bisectors of XYZ and XYZ respectively of XYZ,find OZY and YOZ. (please explain it in detail)

Answer 1

As the sum of all interior angles of a triangle is 180º, therefore, for ΔXYZ,

∠X + ∠XYZ + ∠XZY = 180º

62º + 54º + ∠XZY = 180º

∠XZY = 180º − 116º

∠XZY = 64º

∠OZY == 32º (OZ is the angle bisector of ∠XZY)

Similarly, ∠OYZ == 27º

Using angle sum property for ΔOYZ, we obtain

∠OYZ + ∠YOZ + ∠OZY = 180º

27º + ∠YOZ + 32º = 180º

∠YOZ = 180º − 59º

∠YOZ = 121º

Answer 2

In Triangle XYZ.

XYZ + YZX + ZXY = 180

54 + YZX + 62 = 180

YZX = 180 - 116

        = 64.


Given that YO is the bisector of XYZ

              = 1/2 * XYZ

             = 1/2 * 54

   OYZ  = 27 degrees.


Given that ZO is the bisector of XYZ

                = 1/2 * 64

     OZY  = 32 degrees.


Now, OYZ + OZY + YOZ = 180

           27 + 32 + YOZ = 180

            59 + YOZ = 180

              YOZ = 121 degrees.


Hope this helps!