The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚
So using theorem we find that
∠A+∠C = 180
x + 108 = 180
x = 180 - 108
x = 72
∠B+∠D = 180
88 + y = 180
y = 180 - 88
y = 92
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The required value of angle x and angle y is 72 and 92 respectively.
Given that,
A figure of the circle has been shown,
A quadrilateral is inscribed in the circle,
Angles in the quadrilateral are given as
∠A = x, ∠B = 82, ∠C = 108 and ∠y
The value of angles x and y is to be determined.
A quadrilateral is an irregular four-sided shape as given in the picture in question.
Since quadrilateral has a property that describes that the sum of opposite angle of the quadrilateral is 180°,
Here in the given quadrilateral sum of angle A + C and angle B + D is equal to 180.
⇒
∠A + ∠C = 180
∠A + 108 = 180
∠A = 72°
Similarly
∠B + ∠D = 180
88 + ∠D = 180
∠D = 92
Thus, the required value of angle x and angle y is 72 and 92 respectively.
Learn more about quadrilateral here: https://brainly.com/question/13805601
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