Question

8. Consider the following parallelogram, Find the values of the unknowns x, y, z
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Answer 1

Answer:

∠B + ∠x = 180° ( the adjacent angles of a parallelogram add up to 180° )

∠x = 180° - ∠B

    = 180° - 100°

    = 80°

∠B = ∠y = 100° ( opposite angles of a parallelogram are equal )

∠x = ∠z = 80° ( opposite angles of a parallelogram are equal )

∠y + ∠z = 180° ( adjacent angles of a parallelogram add up to 180° )

100° + 80° = 180°

∠B + ∠x + ∠y + ∠z = 360° ( angle sum property of a quadrilateral = 360° )

100° + 80° + 100° + 80° = 360° ( verified )

∴ ∠x = 80°

  ∠y = 100°

  ∠z = 80°

HOPE IT HELPS ;)

peace!