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Lines and Angles

In the given ...

Question

In the given figure, $△ A B C$ is inscribed in a circle and the bisector of $∠ A$ meets BC in D and the circle in E. $∠ E C D = 30^{\circ}$ , what is $∠ A$ ?

60^{\circ}

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45^{\circ}

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70^{\circ}

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150^{\circ}

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Solution

The correct option is A $60^{\circ}$
$∠ A B E = ∠ B C E = 306^{0}$ (Angles in the same segments are equal )
$∴ ∠ B A C = 2 \times ∠ B A E = 2 \times 30^{\circ} = 60^{\circ} (∵ A E b i s e c t s ∠ B A C)$

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Similar questions

$I n t h e g i v e n f i g u r e, △ A B C i s i n s c r i b e d i n a c i r c l e . T h e b i s e c t o r o f ∠ B A C m e e t s B C a t D a n d t h e c i r c l e a t E, i f E C i s j o i n e d t h e n ∠ E C D = 30^{0} . F i n d ∠ B A C .$

Q. In the given figure,

△

ABC is inscribed in a circle. The bisector of

∠

BAC meets BC at D and the circle at E. If EC is joined then

∠

ECD = 30

^{o}

. Yhe value of

∠

BAC is

Q. In the given figure,

△ A B C

is inscribed in a circle. The bisector of

∠ B A C

meets BC at D and the circle at E. If EC is joined and

∠ E C D

= 30^{o}

, find

∠ B A C

Q. In the given figure,

Δ A B C

is inscribed in a circle. The bisector of

∠ B A C

meets BC at D and the circle at E. If EC is joined then

∠ E C D = 30^{o}

. Find

∠ B A C

Q. In the given figure, ∆ABC and ∆DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°.
(a) 50°
(b) 60°
(c) 70°
(d) 80°

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In the given figure, △ABC is inscribed in a circle and the bisector of ∠A meets BC in D and the circle in E.∠ECD=30∘, what is ∠A?

The correct option is A 60∘∠ABE=∠BCE=3060 (Angles in the same segments are equal )∴∠BAC=2×∠BAE=2×30∘=60∘(∵AEbisects∠BAC)

In the given figure, $△ A B C$ is inscribed in a circle and the bisector of $∠ A$ meets BC in D and the circle in E. $∠ E C D = 30^{\circ}$ , what is $∠ A$ ?

The correct option is A $60^{\circ}$
$∠ A B E = ∠ B C E = 306^{0}$ (Angles in the same segments are equal )
$∴ ∠ B A C = 2 \times ∠ B A E = 2 \times 30^{\circ} = 60^{\circ} (∵ A E b i s e c t s ∠ B A C)$