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Observe the following figure and the value of $x$ from the choices given below is-

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30 °

40 °

50 °

60 °

answer is A.

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Detailed Solution

It is given that a figure with some angles.
Question Image

We have to find the value of

x

.
Consider the triangle

A B E

.
It is known that the sum of the angles of the triangle is

180 °

. So that,

∠ B A E + ∠ B E A + ∠ A B E = 180 °

Substitute the known values from the figure,

75 ° + ∠ B E A + 65 ° = 180 °

∠ B E A + 140 ° = 180 °

∠ B E A = 180 ° − 140 °

∠ B E A = 40 °

Since opposite angles are equal,

∠ B E A = ∠ C E D

∠ C E D = 40 °

Consider the triangle

C D E

.
It is known that the sum of the angles of the triangle is

180 °

∠ C D E + ∠ C E D + ∠ E C D = 180 °

Substitute the known values from the figure,

x + 40 ° + 110 ° = 180 °

x + 150 ° = 180 °

x = 180 ° − 150 °

x = 30 °

The value of

x

30 °

.
Hence option 1 is correct.

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