Angles A, B and C of the inscribed quadrilateral ABCD are 2: 3: 4. Find Angle D.
| July 8, 2021 | education
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 = 2 * X, B = 3 * X, C = 4 * X.
2 * X + 4 * X = 180.
X = 180/6 = 30.
Then:
3 * 30 + D = 180.
D = 180 – 90 = 90.
Answer: Angle D = 90.
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