The diameter AB of the circle is perpendicular to the chord FD. It is known that the angle FBD = 100 degrees. Calculate the degree measures of the angles of the triangle BAD.
It is known that the sum of the opposite interior angles of a convex quadrilateral is 180 degrees.
From here we find the value of the angle FAD.
FAD + FBD = 180º.
FAD + 100º = 180º.
FAD = 80 °.
Since the diameter AB is perpendicular to the chord FD, the triangles FAD and FBD are isosceles.
Therefore, the angle BAD = FAD / 2 = 80 ° / 2 = 40 °, the angle ABD = FBD / 2 = 100 ° / 2 = 50 °.
angle ADB = 180º – (BAD + ABD) = 180º – (40 ° + 50 °) = 90 °.
Answer: BAD = 40 °, ABD = 50 °, ADB = 90 °.
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