Angles A, B, C of a quadrilateral ABCD inscribed in a circle are 3: 4: 7

Angles A, B, C of a quadrilateral ABCD inscribed in a circle are 3: 4: 7, respectively. Find the degree measure of the angle D of this quadrangle.

Since the quadrilateral is inscribed in a circle, it is convex. The sum of the opposite angles of a convex quadrilateral is 180.

A + C = 180.

B + D = 180.

Let’s take one part of the ratio of the angles as X, then A = 3 * X, B = 4 * X, C = 7 * X.

A + C = 180.

3 * X + 7 * X = 180.

X = 180/10 = 180.

Then:

B + D = 180.

4 * 18 + D = 180.

D = 180 -72 = 108.

Answer: Angle D = 108.



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