The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.
What is a circle?
It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
DE is tangent to circle C, at point F.
Then prove that angle ∠FEC and angle ∠ECF are complementary angles.
We know that the radius of the circle and the tangent on the circle make a right angle at the circumference.
Then angle ∠EFC will be 90°.
The sum of all interior angles of the triangle is 180°. Then we have
∠FEC + ∠ECF + ∠EFC = 180°
∠FEC + ∠ECF + 90° = 180°
∠FEC + ∠ECF = 90°
The sum of angle ∠FEC and angle ∠ECF is 90°. Then they are complementary angles.
More about the circle link is given below.
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