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From the following choices, the value of $x$ in the following figure with angles $∠ E A F = 60 °$ and $∠ A C D = 115 °$ is-

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45 °

35 °

65 °

55 °

answer is D.

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Detailed Solution

Given,

∠ E A F = 60 °

and

∠ A C D = 115 °

.
We have to find the value of

x

.
Consider the given figure, since opposite angles in a triangle

A B C

are equal,

∠ B A C = ∠ E A F

∠ BAC = 60 °

Δ A B C

, the exterior angle is equal to the addition of two interior opposite angles.

∠ A B C + ∠ B A C = ∠ A C D

Substitute the known values from the figure,

x + 60 ° = 115 °

x = 115 ° − 60 °

x = 55 °

The value of

x

55 °

.
Hence option 4 is correct.

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