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The sides $B C, B A$ and $C A$ of $Δ A B C$ have been produced to $D, E$ and $F$ respectively, as shown in the given figure. Then, the value of $∠ B$ is from the following choices is-

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35 °

45 °

65 °

75 °

answer is D.

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Detailed Solution

It is given that the figure with some marked angles.
Question Image

We have to find

∠ B

.
Consider the figure, vertically opposite angles are equal, so,

∠ B A C = ∠ F A E

∠ B A C = 35 o

The linear pairs are

∠ B C A, ∠ A C D

∠ B C A + ∠ A C D = ∠ B C D

Substitute the known values from the figure,

∠ B C A + 110 ° = 180 °

∠ B C A = 180 ° − 110 °

= 70 °

Consider the triangle

A B C

∠ A + ∠ B + ∠ C = 180 °

Substitute the known values from the figure,

35 ° + ∠ B + 70 ° = 180 °

105 ° + ∠ B = 180 °

∠ B = 180 ° − 105 °

∠ B = 75 °

The value of

∠ B

75 °

.
Hence option 4 is correct.

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