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°.
<h3>What is a cyclic quadrilateral?</h3>
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
#SPJ1
