2026 · Q51
In a cyclic quadrilateral ABCD, ∠A = (4x + 3)°, ∠B = (3y + 9)°, ∠C = (4y − 3)°, ∠D = (5x − 10)°. What is ∠A + ∠B equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A200°
- B190°
- C180°
- D170°
Explanation
For any parallelogram, and hence any rhombus, the parallelogram law states that the sum of the squares of the diagonals equals four times the square of the side. Here that gives AC² + BD² = 4·AB² = 4·100 = 400. This uses only the given side length, so the question is answerable without either statement, option D.