Question

Lines CD and DE are tangent to circle A shown below.
If Arc CE is 126°, what is the measure of ∠CDE?

126°

63°

117°

54°

Answer 1

what do the sum of the angles of a four sides poly add up to?

Answer 2

360

Answer 3

then lets add

x + 90 + 90 + 126 = 360 ... solve for x

Answer 4

54

Answer 5

x + 90 + 90 + 126 = 360

x + 126 = 180

x + 6 = 60 ... 54 is what i get too

Answer 6

Ok s so it would be 54

Answer 7

another way to do it is with a mean of subtended arcs :)

if we average the subtended arc .. such that the 126 is inverted so its negative we get:\[x=\frac{(360-126)-126}{2}=\frac{108}{2}=54\]