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The value of angle Q ∠Q from the diagram given is 66°

From the diagram ;

  • Angle below R  = 38° (alternate angles with the angle marked 38°)

  • Let the angle vertically opposite angle Q = v

  • 76 + v + 38 = 180° (sum of angles on a straight line)

  • 114 + v = 180°

  • v = 180° - 114° = 66°

  • ∠Q = ∠v = 66° ( vertically opposite angles).

Therefore, the value of angle Q is 66°

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