One of the angles of a triangle is two-third of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 5 : 7 respectively. What is the value of second largest angle of the triangle?

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One of the angles of a triangle is two-third of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 5 : 7 respectively. What is the value of second largest angle of the triangle?

A$25^∘$

B$40^∘$

C$35^∘$

DCannot be determined

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Correct answer is: ${35}^{\circ }$ Explanation: Sum of adjacent angles of a parallelogram = ${180}^o$ Therefore, One of the angles of triangle $=\frac{2}{3}\times {180}^{\circ }={120}^{\circ }$ Sum of three angles of a triangle = ${180}^o$ Therefore, 5x + 7x = 180 - 120 => 12x = 60 => x = 5   Second angle of triangle =  $5\times 5={25}^{\circ }$ Third angle of triangle = $7\times 5={35}^{\circ }$ The second largest angle of triangle = ${35}^o$ Nithin ? answered Aug 13 '2022 at 20:7 All Comments

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