Question

ABCD is a parallelogram in which ∆C is equal to 75° find the other angle.

Answer 1

A parallelogram is a special kind of parallelogram wherein opposite sides apart from being parallel are equal as well.

Characteristics of a parallelogram:
1. Opposite sides are parallel
2. Opposite sides are equal
3. Opposite angles are equal
4. Adjacent angles are supplementary, i.e. they sum to 180 °

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In //gm ABCD,
If angle C = 75 ° , angle A = angle C = 75 °
Reason: Opposite angles in a parallelogram are equal

If angle C = 75 ° , angle B = 180 ° - angle C = 180 ° - 75 ° = 105 °
Reason: Adjacent angles in a parallelogram are supplementary.

If angle B = 105 ° , angle D = angle B = 105 °
Reason: Opposite angles of a parallelogram are equal.

Therefore,

angle A = 75 °
angle B = 105 °
angle C = 75 °
angle D = 105 °

Answer 2

angle C = angle A = 75 degree (opposite angles of a IIgm are equal).
angle D + angle A = 180 degree (adjacent angles of a IIgm add upto 180 degree)
75 + D = 180
D = 180 - 75
D = 105 degree
angle D = angle B = 105 degree (opposite angles of a IIgm are equal)
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