Answer:
arc CD = 160°
Step-by-step explanation:
The measures of the arcs on the circle = 360° , then
arc CD = 360 - AC - AD = 360 - 3x - 7x = 360 - 10x
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The measure of the secant- tangent angle ABC is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (7x - 3x) = 40 ( multiply both sides by 2 to clear the fraction )
7x - 3x = 80
4x = 80 ( divide both sides by 4 )
x = 20
Then
CD = 360 - 10x = 360 - 10(20) = 360 - 200 = 160°
