In the figure- PC is the tangent to the circle- If - BPC - 60- and - APB - 55- then find - ABP -

The correct option is C 65^∘ Using Tangent Chord theorem, ∠ APD nbsp;= ∠ ABP ∠ APD = 180^∘ 55^∘ nbsp;60^∘ = nbsp;65^∘ Therefore ∠ ABP = ∠ APD nbsp ...

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Standard X

Mathematics

Angles in Alternate Segments

In the figure...

Question

In the figure, PC is the tangent to the circle. If $∠ B P C$ = $60^{\circ}$ and $∠ A P B$ = $55^{\circ}$ , then find $∠ A B P$ .

$55^{\circ}$

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$60^{\circ}$

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$65^{\circ}$

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$70^{\circ}$

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Solution

The correct option is C
$65^{\circ}$

Using Tangent-Chord theorem, $∠ A P D$ = $∠ A B P$

$∠ A P D = 180^{\circ} - 55^{\circ} - 60^{\circ} = 65^{\circ}$

Therefore $∠ A B P$ = $∠ A P D$

= $65^{\circ}$

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In the figure, PC is the tangent to the circle. If ∠BPC = 60∘ and ∠APB = 55∘, then find ∠ABP .

The correct option is C 65∘ Using Tangent-Chord theorem, ∠APD = ∠ABP ∠APD=180∘−55∘−60∘=65∘ Therefore ∠ABP = ∠APD = 65∘

In the figure, PC is the tangent to the circle. If $∠ B P C$ = $60^{\circ}$ and $∠ A P B$ = $55^{\circ}$ , then find $∠ A B P$ .

The correct option is C
$65^{\circ}$

Using Tangent-Chord theorem, $∠ A P D$ = $∠ A B P$

$∠ A P D = 180^{\circ} - 55^{\circ} - 60^{\circ} = 65^{\circ}$

Therefore $∠ A B P$ = $∠ A P D$

= $65^{\circ}$