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?
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: \(35^∘\)
Explanation:
Sum of adjacent angles of a parallelogram = \(180^o\)
Therefore, One of the angles of triangle
\(=\Large \frac{2}{3} \times 180 ^{\circ} = 120 ^{\circ}\)
Sum of three angles of a triangle = \(180^o\)
Therefore, 5x + 7x = 180 - 120
=> 12x = 60 => x = 5
Second angle of triangle = \(\Large 5 \times 5 = 25 ^{\circ}\)
Third angle of triangle = \(\Large 7 \times 5 = 35 ^{\circ}\)
The second largest angle of triangle = \(35^o\)
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