If three angles of a quadrilateral are (3y -x - z)°, 3x°, (2z - 2y - x)°, find the fourth angle in terms of x, y and z

  • A (360 - x- y - z)°
  • B (360 + x + y - z)°
  • C (180 - x + y + z)°
  • D (180 - x + y + z)°
jamb 1994mathematics

The correct answer is A. (360 - x- y - z)°

The sum of the angles in a quadrilateral is always \(360°\). Therefore, the fourth angle (\(A\)) can be found by subtracting the sum of the given three angles from \(360°\):

\(A = 360° - ((3y - x - z)° + 3x° + (2z - 2y - x)°)\)

Simplify the expression inside the parentheses:

\(A = 360° - (3y - x - z + 3x + 2z - 2y - x)°\)

Combine the terms:

\(A = 360° - (2y + 2x + x + z)°\)

Simplify further:

\(A = 360° - (3x + 2y + z)°\)

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