If the ratio of four angles of a quadrilateral is ∠A : ∠B : ∠C : ∠D = 2 : 3 : 5 : 8, what is the value of ∠B?
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A.
60∘
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B.
90∘
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C.
50∘
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D.
40∘
Correct Answer:
A. 60∘
Explanation:
The correct answer is Option A: 60 degrees.
In a quadrilateral, the sum of all internal angles is always 360 degrees. Given the ratio of the angles as 2:3:5:8, we can represent the measures as 2x, 3x, 5x, and 8x. By setting up the equation 2x + 3x + 5x + 8x = 360, we find that 18x = 360, which simplifies to x = 20. To find the value of angle B, which corresponds to the second part of the ratio (3x), we multiply 3 by 20, resulting in 60 degrees.
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