Question 1208907: In the diagram, AB is the diameter of the circle, and E is the centre. Find the measure of angle D, in degrees.
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Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
Angle C is the right angle, since it is an inscribed angle
leaning on the diameter of the circle.
Hence, angle B in triangle ABC is 90 - 30 = 60 degrees.
Since the lines BC and DE are parallel, we conclude that the angle DEB is 60 degrees.
Hence, the angle ADE is 180-60 = 120 degrees.
Triangle ADE is an isosceles triangle; therefore, angle D is half of 180-120 = 60 degrees.
ANSWER. Angle D is 60/2 = 30 degrees.
Solved.
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