The ratio between the three angles of a quadrilateral is 1 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

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The ratio between the three angles of a quadrilateral is 1 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

A$120^∘ $

B$90^∘$

C$110^∘$

D$100^∘$

Nithin ? Aug 13 '2022 at 10:54

Correct answer is: \(120^∘\)

Explanation:

\(x+ 4x+ 5x+ 60 = 360^∘ \)

\(\implies 10x = 300^∘\)

\(\implies x = 30\)

\(\text{Therefore, Required difference} = 5x - x = 4x\)

\(= \Large 4 \times 30 = 120 ^{\circ}\)

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Correct answer is: \(120^∘\) Explanation: \(x+ 4x+ 5x+ 60 = 360^∘ \) \(\implies 10x = 300^∘\) \(\implies x = 30\) \(\text{Therefore, Required difference} = 5x - x = 4x\) \(= \Large 4 \times 30 = 120 ^{\circ}\) Nithin ? answered Aug 13 '2022 at 10:54 All Comments

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