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Question

In fig 5.24, ABCD is a parallelogram. ADB = 40°, ABD = 30°, find the measure of BAD, DCB, ADC and ABC.

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Solution

In ΔABD, we have:

BAD + ADB + ABD = 180° ...[Angle addition property of triangle]
BAD + 40° + 30° = 180°
BAD + 70° = 180°
BAD = 180° – 70°
BAD = 110°

In parallelogram ABCD, BAD and DCB are opposite angles and we know that opposite angles in a parallelogram are congruent to each other.

Thus, we have:
DCB = BAD = 110°
BAD + ADC = 180° [In a parallelogram, adjacent angles are supplementary.]
BAD = 110°
We have:
110o + ADC = 180°
ADC = 180° – 110°
ADC = 70°
ABC = ADC = 70° [Opposite angles of a parallelogram are congruent to each other.]
Thus, we get:
BAD = 110°, DCB = 110°, ADC = 70° and ABC = 70°

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