In the given figure- - ABC - 69- ACB - 31- Find - BDC

Given ∠ ABC = 69^∘,∠ ACB = 31^∘ In the triangle ABC, ∠ ABC +∠ ACB+∠ BAC = 180^∘ nbsp; nbsp; nbsp; [Angle sum property of Triangle] 69^∘+31^∘+∠ BAC = 180^ ...

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Standard IX

Mathematics

Introduction to Circles

In the given ...

Question

In the given figure, $∠ A B C = 69^{\circ}, ∠ A C B = 31^{\circ} . F i n d ∠ B D C$

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Solution

Given
$∠ A B C = 69^{\circ}, ∠ A C B = 31^{\circ}$
In the triangle ABC,
$∠ A B C + ∠ A C B + ∠ B A C = 180^{\circ}$ [Angle sum property of Triangle]
$69^{\circ} + 31^{\circ} + ∠ B A C = 180^{\circ}$
$100^{\circ} + ∠ B A C = 180^{\circ}$
$∴ ∠ B A C = 180^{\circ} - 100^{\circ}$
$\Rightarrow ∠ B A C = 80^{\circ}$
$∠ B A C = ∠ B D C = 80^{\circ}$ [Angles in the same segment are equal]
$∴ ∠ B D C = 80^{\circ}$

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In the given figure, ∠ABC=69∘,∠ACB=31∘.Find∠BDC

Given ∠ABC=69∘,∠ACB=31∘ In the triangle ABC, ∠ABC+∠ACB+∠BAC=180∘ [Angle sum property of Triangle] 69∘+31∘+∠BAC=180∘ 100∘+∠BAC=180∘ ∴∠BAC=180∘−100∘ ⇒∠BAC=80∘ ∠BAC=∠BDC=80∘ [Angles in the same segment are equal] ∴∠BDC=80∘

In the given figure, $∠ A B C = 69^{\circ}, ∠ A C B = 31^{\circ} . F i n d ∠ B D C$