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Sagot :

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°

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