# The diameter AB of the circle is perpendicular to the chord FD. It is known that the angle FBD = 100

March 23, 2021 | education

| **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 °.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.