Question

CH name lines and angles class 9

Answer 1

angle 1= 180- anglePBO- angleABC
1=180-angle1-angleABC
2(angle1)=180-angleABC
angle1=90-angleABC/2............(1)

2(angle2)=180-angleACO
angle2=90-angleACO/2................(2)

In triangle BOC

angle2+angle1+angleBOC=180 (ASP OF TRI.)

PUTTING VALUE OF (1) AND (2)

90-angleACO/2+90-angleABC/2+angleBOC=180

180-angleACO/2-angleABC+angleBOC=180

angleBOC=(angleACO+angleABC)/2...........(A)


IN TRIANGLE ABC

angleA+angleACO+angleABC=180 (ASP)
angleACO+angleABC=180-angleA.......(B)


PUT VALUE OF (B) IN (A)

angleBOC=(180-angleA)/2
angleBOC=90-angleA/2

PROOVED



HOPE IT HELPS YOU.