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​ Quadrilateral ABCD ​ is inscribed in this circle.



What is the measure of angle C?

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Image shows a circle with inscribed quadrilateral A B C D. The measure of angle A is 2 x plus 3 degrees. The measure of angle B is 2 x minus 4 degrees. The measure of angle D is 3 x plus 9 degrees.

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Answer:

107

Step-by-step explanation:

First note that this quadrilateral is cyclic.

One property of cyclic quadrilaterals is that opposite angles add up to 180.

since B and D are opposite angles, we can add them and set that to 180. we get that 5x+5=180, so x=35. Now, substituting 37 for x for all the angles, we get

A=73

B=66

D=114

To find C, notice that A and C are opposite angles. This means they add up to 180

73+C=180, C=107

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