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In the given figure, sides $C B$ and $B A$ of $Δ A B C$ have been produced to $D$ and $E$ respectively such that $∠ A B D = 110 °$ and $∠ C A E = 135 °$ . Then the value of $∠ A C B$ from the following choices is

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65 °

55 °

45 °

35 °

answer is A.

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Detailed Solution

It is given that

∠ A B D = 110 °

and

∠ C A E = 135 °

.
It is to find the value of

∠ A C B

.
Sum of angles on either side of a line is

180 °

.
Hence, for the line

C D

∠ A B D + ∠ A B C = 180 °

Solve this equation to find

∠ A B C

.
Substitute the known values from the figure,

110 ° + ∠ A B C = 180 °

∠ A B C = 180 ° − 110 °

∠ A B C = 70 °

Calculate the value of

∠ A C B

using the postulate that the sum of opposite interior angles
of a triangle is equal to the exterior angle.
Hence,

∠ A B C + ∠ A C B = ∠ C A E

Substitute the known values from the figure,

70 ° + ∠ A C B = 135 °

∠ A C B = 135 ° − 70 °

∠ A C B = 65 °

The value of

∠ A C B

65 °

.
Hence option 1 is correct.

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