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प्रश्न
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
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उत्तर
\[\text{ Two adjacent angles of a parallelogram add up to } 180° . \]
\[\text{ Let x be the angle } . \]
\[ \therefore x + \frac{2x}{3} = 180°\]
\[\frac{5x}{3} = = 180°\]
\[x = 72°\]
\[\frac{2x}{3} = \frac{2 \times 72°}{3} = 108°\]
\[\text{Thus, two of the angles in the parallelogram are 108° and the other two are }72° .\]
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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
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(iii) \[\angle DCE = \frac{1}{2}\angle C\]
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(v) CE || AF
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