AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC. B is a point on the circumference of the circle in the other semicircle ∠CBE = 75°. What is the measure (in degrees) of ∠CED?
Answer & explanation
Correct answer: option 4
Concept Used
The diameter of a circle subtends an angle of 90 degree at any point on the circle.
Angles formed by the endpoints of the chord in either major or minor segments are always equal.
Calculations
\(\angle\)CBE = \(\angle\)CAE = \({75}^\circ\)
\(\angle\)AEC = \({90}^\circ\)
So,
\(\angle\)ECA = \({180}^\circ\) - \({90}^\circ\) - \({75}^\circ\) = \({15}^\circ\)
Now,
ED is parallel to AC
So,
\(\angle\)ECA = \(\angle\)CED = \({15}^\circ\)
Therefore, \(\angle\)CED is \({15}^\circ\)