The chords AB and CD of the circle meet at point E. find the angle BEC, if arc AD = 54 degrees, arc BC = 70 degrees.
| September 2, 2021 | education
Consider the ACE triangle.
The EAC angle is the angle BAC inscribed in a circle, resting on the arc BC, the degree measure of which is 70, then the value of the angle EAC = 70/2 = 450.
The ACE angle is the inscribed angle of the DСA, resting on the AD arc, the degree measure of which is 54, then the ECA angle = 54/2 = 270.
The sum of the interior angles of the triangle is 180, then the angle AEC = (180 – 45 – 27) = 108.
Angles AEC and BEC are adjacent, the sum of which is 180, then the angle BEC = (80 – 108) = 72.
Answer: The angle BEC is 72.
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