Answer:
[tex] m\angle BOA = 80\degree[/tex]
Step-by-step explanation:
PA and PB are tangents to the circle with center O at points A and B respectively.
[tex]\therefore OA \perp PA\:\: \& OB \perp PB....(\because tangent\perp radius)\\\therefore m\angle OAP=m\angle OBP = 90\degree\\m\angle APB = 100\degree\\OAPB \: is \: a\: quadrilateral\\\therefore m\angle APB+m\angle OAP+m\angle OBP+m\angle BOA = 360\degree\\\therefore 100\degree + 90\degree+ 90\degree+ m\angle BOA = 360\degree\\\therefore 280\degree + m\angle BOA = 360\degree\\\therefore m\angle BOA = 360\degree-280\degree \\\huge\red{\boxed{\therefore m\angle BOA = 80\degree}}[/tex]
