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  • ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.

Q 6. $\mathrm{ABCD}$ is a cyclic quadrilateral whose diagonals intersect at a point E . If $\angle D B C=70^{\circ}, \angle B A C$ is $30^{\circ}$, find $\angle B C D$. Further, if $A B=B C$, find $\angle E C D$.

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best_answer

$=\angle B D C=\angle B A C \quad$ (angles in the same segment are equal )
$\angle B D C=30^{\circ}$
In $\triangle B D C$
$\angle B C D+\angle B D C+\angle D B C=180^{\circ}$
$\Rightarrow \angle B C D+30^{\circ}+70^{\circ}=180^{\circ}$
$\Rightarrow \angle B C D+100^{\circ}=180^{\circ}$
$\Rightarrow \angle B C D=180^{\circ}-100^{\circ}=80^{\circ}$
If $\mathrm{AB}=\mathrm{BC} \text {, then }$
$\angle B C A=\angle B A C$

$\Rightarrow \angle B C A=30^{\circ}$
Here, $\angle E C D+\angle B C E=\angle B C D$

$\Rightarrow \angle E C D+30^{\circ}=80^{\circ}$
$\Rightarrow \angle E C D=80^{\circ}-30^{\circ}=50^{\circ}$

 

 

 

 

 

 

 

 

 

 

 

 

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seema garhwal

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