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Locus of the Points Equidistant From Two Given Points

Given, a quad...

Question

Given, a quadrilateral $A B C D$ is inscribed in a circle as shown in the figure
If $∠ B = 125^{\circ}$ , then $∠ E$ is equal to ..........

55^{\circ}

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125^{\circ}

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130^{\circ}

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{62.5}^{\circ}

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Solution

The correct option is A $55^{\circ}$
$A B C D i s a g i v e n q u a d i l a t e r a l ∠ B = 125 (G i v e n) ∠ B + ∠ D = 180 (S u m o f o p p o s i t e a n g l e s o f c y c l i c q u a d i l a t e r a l i s 180 ∠ D = 180 - ∠ B = 180 - 125 = 55 ∠ D = 55.... (1) N o w ∠ D = ∠ E (A n g l e s o n t h e s a m e s e g m e n t a r e e q u a l) \Rightarrow ∠ E = 55 [F r o m (1)] H e n c e o p t i o n A i s t h e c o r r e c t a n s w e r$

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Similar questions

A B C D

E C B A

∠ B = 125^{\circ},

∠ E .

ABCD

∠ D = 55^{\circ}

∠ E

A B C D

A B

∠ A D C = 130^{o}

m ∠ B A C =

In the given figure, equilateral $△$ ABC is inscribed in a circle and ABCD is a quadrilateral, as shown. Then $∠$ BDC = ?

(a) $90^{\circ}$

(b) $60^{\circ}$

(d) $150^{\circ}$

∠ A D C = 130^{\circ}

∠ A B C

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