The ratio between the adjacent angles of a parallelogram is 7 : 8 respectively. Also the ratio between the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of parallelogram and second largest angle of the quadrilateral?

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The ratio between the adjacent angles of a parallelogram is 7 : 8 respectively. Also the ratio between the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of parallelogram and second largest angle of the quadrilateral?

A168°

B228°

C156°

D224°

Nithin ? Aug 14 '2022 at 11:8

Correct answer is: 168°

Explanation:

 

Let the adjacent angles be \(7x^∘\text{and }8x^∘\)

Therefore, 7x + 8x = 180

=> 15x = 180

=> x = 12

Therfore, Smaller angle = 7 x 12 = 84°

Again. 5y + 6y + 7y + 12y = 360°

=> 30y = 360°

= y = \(\frac{360}{30}\)

Therefore, Second largest angle of the quadrilateral

= 7×12 = \(84^o\)

 

Therefore, Required sum = \(84 + 84 = 168^o\)

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Correct answer is: 168° Explanation:   Let the adjacent angles be \(7x^∘\text{and }8x^∘\) Therefore, 7x + 8x = 180 => 15x = 180 => x = 12 Therfore, Smaller angle = 7 x 12 = 84° Again. 5y + 6y + 7y + 12y = 360° => 30y = 360° = y = \(\frac{360}{30}\) Therefore, Second largest angle of the quadrilateral = 7×12 = \(84^o\)   Therefore, Required sum = \(84 + 84 = 168^o\) Nithin ? answered Aug 14 '2022 at 11:8 All Comments

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