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Angle Subtended by Diameter on the Circle

In the given ...

Question

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and $∠$ EAB = $63^{o}$ . Calculate : (i) $∠$ EBA, (ii) $∠$ BCD.

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Solution

(i) $∠ A E B = 90^{o} (a n g l e i n t h e s e m i c i r c l e)$

$∠ E B A = 180^{o} - 90^{o} - 63^{0} = 27^{o}$

(ii) $E D ∥ A B$

$∠ D E B - ∠ E B A = 27^{o}$ (alternate angles)

EBCD is a cyclic quadrilateral

$∠ D E B + ∠ D C B = 180^{o}$

$∠ D C B = 180^{o} - 27^{o} = 153^{o}$

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