Question

Find the values of x and y. then find the measures of the interior angles of the polygon​

Answer 1

The value of x and y are 9 and 6. Then the measure of the angles ∠A, ∠B, ∠C, and ∠D will be 54°, 36°, 126°, and 144°.

What is a cyclic quadrilateral?

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

We know the sum of the opposite angle of the cyclic quadrilateral is 180°.

Then we have

14x + 9y = 180 ...1

4x + 24y = 180 ...2

By solving the equations 1 and 2, we have

x = 9 and y = 6

Then the measure of the angle will be

∠A = 9y = 9 × 6 = 54°

∠B = 4x = 4 × 9 = 36°

∠C = 14x = 14 × 9 = 126°

∠D = 24y = 24 × 6 = 144°

More about the cyclic quadrilateral link is given below.

brainly.com/question/15061291

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