Question

In the figure angle X=72° , angle XYZ=46° . If YO and ZO are bisectors of angle xyz and angle xzy respectively of triangle XYZ , find angle OYZ and angle YOZ​.
class:- 9th​

Answer 1

Step-by-step explanation:

In the figure angle X=72° , angle XYZ=46° . If YO and ZO are bisectors of angle xyz and angle xzy respectively of triangle XYZ , find angle OYZ and angle YOZ

Step-by-step explanation:

In fig YO and ZO are respectively the bisector , and bisector bisect the angle in two equal parts so

angle (OYZ) = 1/2 angle (XYZ)

angle (OYZ) = 1/2 (46) = 23 DEGREE

NOW IN TRIANGLE XYZ by angle sum property

x+y+z =180

72 +46 +z =180

z = 180 -118

z = 62 degree

1. now apply angle sum property in triangle OYZ

angle (OYZ) + angle (OZY)+ angle (YOZ)= 180

angle (OYZ) + angle (OZY)+ angle (YOZ)= 180

23 +31 + angle (YOZ)= 180

ANGLE (YOZ)= 180-54

=126 DEGREE

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