Question

the angles of a quadrilateral are 2x, 2x+15, 4x-12, 3x-0.5 . Find the value of x and all the angles of quadrilateral.

Answer 1

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As we know ,
the sum of all angles of quadrilateral = 360°
2x + 2x + 15 + 4x - 12 + 3x - 0.5 = 360°
11x + 15 - 12.5 = 360°
11x + 2.5 = 360°
11x = 360° - 2.5
11x = 357.5°
x = 32.5°

1st angle = 2x = 2 × 32.5 = 65°
2nd angle = 2x + 15 = 2 × 32.5 + 15 = 65 + 15 = 80°
3rd angle = 4x - 12 = 4 × 32.5 - 12 = 130 - 12 = 118°
4th angle = 3x - 0.5 = 3 × 32.5 - 0.5 = 97.5 - 0.5 = 97°