Question

Consider the given parallelogram. Find the values of the unknowns x, y, z.

Answer 1

x + 100° = 180° (Adjacent angles are supplementary)

x = 80°

z = x = 80º(Opposite angles are equal)

y = 100° (Opposite angles are equal)

Answer 2

ABCD is a parallelogram in which ∠B = 100° (given)

∴ ∠A + ∠B = 180°   ...[∵ Sum of adjacent angles is 180°]

⇒ z + 100° = 180°

⇒ z = 180° − 100° = 80°

Also ∠B = ∠D and ∠A = ∠C   ...[∵ Opposite angles are equal]

∴ ∠B = 100° = ∠D = y and ∠A = z = 80° = ∠C = x

∴ x = 80°, y = 100°, z = 80°