Question

In fig 6.52, ANGLE X=60° ANGLE XYZ =50° IF YO AND ZO ARE THE BISECTORS OF ANGLE XYZ AND ANGLE XZY FIND ANGLE YOU AND ANGLE OZY

Answer 1

In triangle ABC, AngleX+angleY+angleZ=180 (angle sum) 60+50+Z=180 Z=180-110 Z=70 In triangleOZY, OZY=1/2 of XZY OZY=70/2 OZY=35 OYZ=1/2 of XYZ OYZ=50/2 OYZ=25 AngleYOZ+angleOZY+angleOYZ=180 (angle sum) YOZ+35+25=180 YOZ=180-60 YOZ=120

Answer 2

In ∆XYZ , we have

60 + 50 + XZY = 180°

< XZY = 180° - 110 = 70°

2<OZY = 70

<OZY = 35°

In ∆ OYZ , we have

< OYZ + < OZY + < YOZ = 180°

25 + 35 + < YOZ = 180°

< YOZ = 180° - ( 25 + 35 ) = 180° - 60° = 120° .