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Angles in Same Segment of a Circle

In the given ...

Question

In the given figure, AOC is a diameter and AC is parallel ot ED. If $∠$ CBE = $64^{o}$ , calculate $∠$ DEC.

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Solution

$\angle ABC = 90^o$ (angle in a semi circle)

$\angle ABE = 90^o-64^o = 26^o$

$\angle ABE = \angle ACE = 26^o$ (angles in the same segment)

$AC \parallel ED$

$\therefore \angle DEC = \angle ACE = 26^o$ (alternate angles because AC and ED are parallel to each other and EC is the transversal)

$\\$

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