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Which of the following is the measure of $x °$ ?

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1000

1150

1350

1050

answer is D.

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Detailed Solution

Given figure,
Question Image

Here,

∠ A D C = 1800 − 500 ∠ A D C = 1300

[Linear pair]

∠ D A B = 1800 − 1150 ∠ D A B = 650

[Linear pair]
And, same as

∠ B C D = 1800 − 900 ∠ B C D = 900

[Linear pair]
We know that,
Sum of all the interior angles of an n-sided polygon

= (n − 2) × 1800

, where, n is the number of sides of the given polygon.
Substituting the number of sides in the given polygon n = 4.
Sum of all the interior angles

= (4 − 2) × 1800

Sum of all the interior angles

= 3600

Then,

∠ A D C + ∠ D A B + ∠ B C D + ∠ A B C = 3600

On substituting all values of all the angles,

1300 + 650 + 900 + ∠ A B C = 3600 2850 + ∠ A B C = 3600 ∠ A B C = 3600 − 2850 ∠ A B C = 750

Thus,

x 0

∠ C B F

1800 − 750

On solving,

x 0

∠ C B F

1050

Hence, the value of the exterior angle

x 0

∠ C B F

of the given polygon ABCD is

1050

.
Therefore, option 4 is correct.

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