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In a given figure, the side $BC$ of $△ A B C$ has been extended on both sides-on the left to $D$ and on the right to $E$ and $∠ A B D = 106 °$ and $∠ A C E = 118 °$ , then what is the value of each angle of the triangle?

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∠ A B C = 75 °

∠ A C B = 65 °

, and

∠ B A C = 45 °

∠ A B C = 74 °

∠ A C B = 62 °

, and

∠ B A C = 44 °

∠ A B C = 70 °

∠ A C B = 66 °

, and

∠ B A C = 40 °

∠ A B C = 44 °

∠ A C B = 52 °

, and

∠ B A C = 44 °

answer is B.

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Detailed Solution

Given that

∠ A B D = 106 °

and

∠ A C E = 118 °

Now, considering DC as a straight line,

∠ A B D + ∠ A B C = 180 ° 106 ° + ∠ A B C = 180 ° ∠ A B C = 74 °

-------------(1)
Now, considering BE as a straight line,

∠ A C B + ∠ A C E = 180 ° ∠ A C B + 118 ° = 180 ° ∠ A C B = 62 °

-------------(2)
The sum of the angles of the triangle is

180 °

.
So, from equation (1) and (2),

∠ A B C + ∠ A C B + ∠ B A C = 180 ° 74 ° + 62 ° + ∠ B A C = 180 ° ∠ B A C = 44 °

Therefore,

∠ A B C = 74 °

∠ A C B = 62 °

, and

∠ B A C = 44 °

.
Hence, option (2) is correct.

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In a given figure, the side BC of △ABC has been extended on both sides-on the left to D and on the right to E and ∠ABD= 106 ° and ∠ACE= 118 ° , then what is the value of each angle of the triangle?

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In a given figure, the side $BC$ of $△ A B C$ has been extended on both sides-on the left to $D$ and on the right to $E$ and $∠ A B D = 106 °$ and $∠ A C E = 118 °$ , then what is the value of each angle of the triangle?