9514 1404 393
Answer:
Explanation:
The external angle at A is half the difference of the arcs it intercepts. The inscribed angle y is half the measure of arc CD. The sum of the arcs of a circle is 360°. These relations let us write some equations.
(BC -x°)/2 = ∠A
BC + CD + x° = 360°
y° = CD/2
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Given that BC = 120° and ∠A = 20°, we can use the first equation to find x.
(120 -x)/2 = 20
120 -x = 40 . . . . . multiply by 2
120 -40 = x = 80 . . . . add x-40
Using known values in the second equation gives ...
120 +CD +80 = 360
CD = 160 . . . . . . . subtract 200
Then y is found from the third equation.
160/2 = y = 80