What is the value of x?
a)105
b)130
c)135
d)140
e)145
An inscribed angle is formed by 2 chords.
Since ∠AED is formed by chords AE and DE, ∠AED is an inscribed angle.
Chords AE and ED intercept arc ABCD on the circle.
The degree measurement of an inscribed angle is equal to 1/2 the degree measurement of the intercepted arc.
Since ∠AED = 75º, arc ABCD = 150º.
Since AB=BC=CD, arc AB = arc BC = arc CD.
Since arcs AB, BC and CD together constitute 150º of the circle, arc AB = 50º, arc BC = 50º, and arc CD = 50º.
Since arc BC + arc CD = 50+50 = 100º, arc BAED = 360-100 = 260º.
Arc BAED is intercepted by inscribed angle x.
Since the degree measurement of an inscribed angle is 1/2 the degree measurement of the intercepted arc, x = (1/2)(260) = 130.
The correct answer is
B.
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