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Question
Consider the given parallelogram. Find the values of the unknowns x, y, z.
Solution 1
x + 100° = 180° (Adjacent angles are supplementary)
x = 80°
z = x = 80º(Opposite angles are equal)
y = 100° (Opposite angles are equal)
Solution 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°
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