In the given figure- if - ABC -69- and - ACB -31-Then- enter the value of - BDC in degreesA- 80

The correct option is A 80Given, ∠ ABC=69^∘ and ∠ ACB=31^∘. Using angle sum property in ABC, nbsp; nbsp; ∠ BAC + ∠ ABC +∠ ACB=180^∘. i.e., ∠ BAC + 69^∘+31^ ...

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Standard X

Mathematics

Angles in the Same Segment Are Equal

In the given ...

Question

$In the given figure, if ∠ A B C = 69^{\circ} and$
$∠ A C B = 31^{\circ} .$
$Then, enter the value of ∠ B D C in degrees$

80

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Solution

The correct option is A 80
Given,
$∠ A B C = 69^{\circ}$ and $∠ A C B = 31^{\circ} .$

Using angle sum property in $△ A B C,$
$∠ B A C + ∠ A B C + ∠ A C B = 180^{\circ} .$
$i.e., ∠ B A C + 69^{\circ} + 31^{\circ} = 180^{\circ}$
$⟹ ∠ B A C = 180^{\circ} - 100^{\circ} = 80^{\circ}$

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, if ∠ABC=69∘ and ∠ACB=31∘. Then, enter the value of ∠BDC in degrees 80

The correct option is A 80Given, ∠ABC=69∘ and ∠ACB=31∘. Using angle sum property in △ABC, ∠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∘

$In the given figure, if ∠ A B C = 69^{\circ} and$
$∠ A C B = 31^{\circ} .$
$Then, enter the value of ∠ B D C in degrees$

80