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

Given that ∠ ABC=69^∘ and ∠ ACB=31^∘. Using angle sum property in ABC, we have nbsp; ∠ BAC + ∠ ABC +∠ ACB=180^∘. i.e., nbsp;∠ BAC + 69^∘+31^∘=180^∘ ∠ BAC=18 ...

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Standard IX

Mathematics

Theorem of Equal Angles Subtended by Different Chords

In the given ...

Question

In the given figure, $∠ A B C = 69^{\circ}$ and $∠ A C B = 31^{\circ} .$ Find $∠ B D C .$

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Solution

Given that $∠ A B C = 69^{\circ}$ and $∠ A C B = 31^{\circ} .$
Using angle sum property in $△ A B C,$ we have
$∠ B A C + ∠ A B C + ∠ A C B = 180^{\circ} .$
i.e., $∠ B A C + 69^{\circ} + 31^{\circ} = 180^{\circ}$
$⟹ ∠ B A C = 180^{\circ} - 100^{\circ} = 80^{\circ}$
Now, since the angles in the same segment are equal,
$∠ B A C = ∠ B D C .$
$∴ ∠ B D C = 80^{\circ}$

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

Given that ∠ABC=69∘ and ∠ACB=31∘. Using angle sum property in △ABC, we have ∠BAC+∠ABC+∠ACB=180∘. i.e., ∠BAC+69∘+31∘=180∘ ⟹∠BAC=180∘−100∘=80∘ Now, since the angles in the same segment are equal, ∠BAC=∠BDC. ∴∠BDC=80∘

In the given figure, $∠ A B C = 69^{\circ}$ and $∠ A C B = 31^{\circ} .$ Find $∠ B D C .$