In Fig., AB || CD and AC || BD. Find the values of x, y, z.

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Solution

(i) Since AC || BD and CD || AB, ABCD is a parallelogram.
$∠$ CAB + $∠$ ACD = 180° (Sum of adjacent angles of a parallelogram)
∴ $∠$ ACD = 180° − 65° = 115°
$∠$ CAD = $∠$ CDB = 65° (Opposite angles of a parallelogram)
$∠$ ACD = $∠$ DBA = 115° (Opposite angles of a parallelogram)

(ii) Here,
AC || BD and CD || AB
$∠$ DAC = x = 40° (Alternate interior angle)
$∠$ DAB = y = 35° (Alternate interior angle)

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