The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?
The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?
A160°
B 180°
C190°
D 170°
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Correct answer is: 180°
Explanation:
Sum of the angles of a quadrilateral = 360
Therefore, \(3x + 4x + 5x + 6x = 360\)
\(\implies 18x = 360\)
\(\implies x = \frac{360}{18}= 20\)
Therefore, smallest angle of quadrilateral \( = 3×20 = 60\)
Largest angle of quadrilateral \(= 6×20 = 120\)Therefore, smallest angle of triangle \(= 60× \frac{2}{3}=40\)
Largest angle of triangle \(= 2×40 = 80\)
Therefore, third angle of triangle \(= 180−40−80=60\)
Required sum \(= 60 +120 = 180\)
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