Answer:
Angle BCD is 28°
Explanation:
Given ABC and CDE are tangents
so, Angle OBC and Angel ODC are 90 degrees
this is because "The tangent at any point of a circle and radius through this point are perpendicular to each other"
Angle BFD is twice the angle BOD
because "angel at the center is twice the angle at remaining circumference"
So now,
Angle BOD is 2(76) = 152 degrees
Angle OBC = 90 degrees
Angle ODC = 90 degrees
Angle BCD = ?
Now, BODC is a quadrilateral with the some of all 4 angels equal to 360 degrees
Therefore,
Angle BCD = Total - (Angle BOD + Angel OBC + Angle ODC)
Angle BCD = 360 - (152 + 90 + 90)
Angel BCD = 28 degrees