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Triangle and Sum of Its Internal Angles

In the given ...

Question

In the given figure, value of $x$ is .........

^{o}

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^{o}

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109

^{o}

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Solution

The correct option is D 109 $^{o}$
In triangle $Δ A B C$ ,
$∠ A + ∠ A B C + ∠ B C A = 180^{o}$
$34^{o} + ∠ A B C + 30^{o} = 180^{o}$
$∠ A B C = 116^{o}$
So, $∠ A B C + ∠ C B D = 180^{o}$
$116^{o} + ∠ C B D = 180^{o}$
$∠ C B D = 180^{o} - 116^{o}$
$∠ C B D = 64^{o}$
Now use remote interior angle theorem.
So, $∠ X = ∠ C B D + ∠ D = 64^{o} + 45^{o} = 109^{o}$

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In the given figure, value of x is .........

The correct option is D 109oIn triangle ΔABC,∠A+∠ABC+∠BCA=180o34o+∠ABC+30o=180o∠ABC=116oSo, ∠ABC+∠CBD=180o116o+∠CBD=180o∠CBD=180o−116o∠CBD=64oNow use remote interior angle theorem.So, ∠X=∠CBD+∠D=64o+45o=109o

In the given figure, value of $x$ is .........