The angles of a quadrilateral are in ratio of 3 : 5 : 9 : 7. The second largest angle of the quadrilateral is equal to the largest angle of a triangle. One of the angles of the triangle is $25^∘$. What is the value-of second largest angle of the triangle?

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INSURANCE EXAMS (UIIC) 2011 click here to view all questions

The angles of a quadrilateral are in ratio of 3 : 5 : 9 : 7. The second largest angle of the quadrilateral is equal to the largest angle of a triangle. One of the angles of the triangle is $25^∘$. What is the value-of second largest angle of the triangle?

A$60^∘$

B$50^∘$

C$40^∘$

D$20^∘$

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Correct answer is: ${50}^o$ Explanation: Sum of ratios = 3 + 5 + 9 + 7 = 24 Second largest angle of quadrilateral = $\frac{7}{24}\times 360={105}^{\circ }$ Largest angle of triangle Therefore, Third angle of triangle = $\frac{7}{24}\times 360={105}^{\circ }$ $={180}^{\circ }-{105}^{\circ }-{25}^{\circ }$ $={50}^{\circ }=\text{second largest angle of triangle.}$   Nithin ? answered undefined All Comments

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