In the adjoining figure, chord $E D$ is parallel to the diameter $A C$ of the circle. If $∠ C B E = 65^{\circ}$ , then what is the value of $∠ D E C$ ?

35^{\circ}

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55^{\circ}

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45^{\circ}

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25^{\circ}

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Solution

The correct option is D $25^{\circ}$
$C i r c l e c e n t r e O a n d c h o r d E D ∥ A C a n d ∠ C B E = 65 (G i v e n) ∠ A B C = 90 (A n g l e i n a s e m i c i r c l e) ∠ A B C = ∠ A B E + ∠ C B E \Rightarrow ∠ A B E = ∠ A B C - ∠ C B E = 90 - 65 = 25 ∠ A B E = 25.... (1) N o w ∠ A B E = ∠ A C E (A n g l e s o n s a m e s e g m e n t) \Rightarrow ∠ A C E = 25 ([F r o m (1)] S i n c e A C ∥ E D ∠ A C E = ∠ D E C (A l t e r n a t e a n g l e s a r e e q u a l) \Rightarrow ∠ D E C = 25 H e n c e o p t i o n (D) i s t h e r i g h t a n s w e r$

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Similar questions

In the given figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE= 65°, then ∠DEC =

E D

A C

∠ C B E = 65^{\circ}

∠ D E C

E D

A C

∠ C B E = 65^{\circ} c a l c u l a t e ∠ D E C .

Chord ED is parallel to the diameter AC of the circle. Given ∠CBE=55°, calculate ∠DEC.

∠ C B E = 65^{\circ}

∠ D E C

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