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Equal Angles Subtend Equal Sides

ABC is inscri...

Question

$△ A B C$ is inscribed in a circle. Point $P$ lies on the circle between $A$ and $C$ . If $m (arc A P C) = 60^{\circ}$ and $∠ B A C = 80^{\circ}$ , find $m ∠ A B C .$

65^{\circ}

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30^{\circ}

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42^{\circ}

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16^{\circ}

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Solution

The correct option is B $30^{\circ}$

$∠ A B C$ is the inscribed angle of arc $A P C$ .

Therefore, by Inscribed angle theorem,

$m ∠ A B C = \frac{1}{2} m (arc A P C)$

$m ∠ A B C = \frac{1}{2} \times 60$ ...[Given]

$m ∠ A B C = 30^{\circ}$

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△ABC is inscribed in a circle. Point P lies on the circle between A and C. If m(arcAPC)=60∘ and ∠BAC=80∘, find m∠ABC.

The correct option is B 30∘ ∠ABC is the inscribed angle of arc APC.Therefore, by Inscribed angle theorem,m∠ABC=12m(arcAPC)m∠ABC=12×60 ...[Given]m∠ABC=30∘

$△ A B C$ is inscribed in a circle. Point $P$ lies on the circle between $A$ and $C$ . If $m (arc A P C) = 60^{\circ}$ and $∠ B A C = 80^{\circ}$ , find $m ∠ A B C .$

The correct option is B $30^{\circ}$

$∠ A B C$ is the inscribed angle of arc $A P C$ .

Therefore, by Inscribed angle theorem,

$m ∠ A B C = \frac{1}{2} m (arc A P C)$

$m ∠ A B C = \frac{1}{2} \times 60$ ...[Given]

$m ∠ A B C = 30^{\circ}$