Question

Lx = 52 LXYZ = 64 if YO and ZO are the bisector of LXYZ and LXZY respective . find LOZY and LYOZ​

Answer 1

Answer:

angle x = 52°

angle y = 64°

In triangle XYZ,

angle x + angle y + angle z = 180°. (By ASP)

52 + 64 + z = 180°

116° + z = 180°

z = 180° - 116°

angle z = 64°

given : YO and ZO are bisectors of angle y and z respectively

angle OYZ = 1/2 angle XYZ

angle OYZ = 32°

angle OZY = 1/2 angle XZY

angle OZY = 32°

In triangle OYZ,

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

32° + 32° + YOZ = 180°

64° + YOZ = 180°

YOZ = 180° - 64°

angle YOZ = 116°