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If three angles of a quadrilateral are each equal to $75 °$ , then determine the fourth angle and choose the option which represents the same.

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150 °

135 °

45 °

75 °

answer is B.

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Detailed Solution

Given, three angles of a quadrilateral are each equal to

75 °

.
The angle sum property of a quadrilateral states that the sum of all the interior angles of a quadrilateral is always

360 ∘

.
Now, let the measure of the fourth angle be x.
Then, by the angle sum property, we have,

75 ∘ + 75 ∘ + 75 ∘ + x = 360 ∘ 225 ∘ + x = 360 ∘ x = 360 ∘ − 225 ∘ x = 135 ∘

So, the fourth angle of the quadrilateral measures

135 ∘

.
Hence, the correct option is (2).

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