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Question
ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D.
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Solution
\[\text{ Opposite angles of a parallelogram are equal } . \]
\[ \therefore \angle C = 70° = \angle A . \]
\[ \angle B = \angle D\]
\[\text{ Also, the sum of the adjacent angles of a parallelogram is } 180°. \]
\[ \therefore \angle A + \angle B = 180°\]
\[70° + \angle B = 180°\]
\[\angle B = 110°\]
\[ \therefore \angle B = 110°, \angle C = 70°\text{ and } \angle D = 110°\]
RELATED QUESTIONS
In the following Figure ABCD is a arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:
(i) ∠A = ∠C
(ii) \[\angle FAB = \frac{1}{2}\angle A\]
(iii) \[\angle DCE = \frac{1}{2}\angle C\]
(iv) \[\angle CEB = \angle FAB\]
(v) CE || AF
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