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In figure, AB, CD and EF are three lines concurrent at O. Find the value of x.

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22°

20°

18°

16°

answer is C.

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Detailed Solution

When two lines intersect each other at a point, then vertical opposite angles are equal. A straight angle or a linear angle is equal to

180 °

.
Note the given conditions.
Question Image

Now, from figure we have AB, CD and EF are intersecting lines, at point O.
And angles are AOD=2x

… .. (1)

COE=3x

… … (2)

⇒ ∠ B O F = 5 x … … (3)

Compute vertically opposite angle, and apply formulae of tip.
Now, from figure we have line AB and EF are intersecting lines, then vertically opposite angles are equal,

⇒ ∠ A O E = ∠ B O F

∴ ∠ A O E = 5 x … … (4)

Evaluate the sum of angles at linear angle.
Now, the angle

∠ C O D

is a straight angle.

⇒ ∠ C O D = 180 °

⇒ ∠ C O E + ∠ E O A + ∠ A O D = 180 °

⇒ 3 x + 5 x + 2 x = 180 °

⇒ 10 x = 1800

∴ x = 18 °

Therefore, value of x is

18 °

.
Therefore, option (3) is correct.

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