Question

The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. the smallest angle of a triange is one-fourth the largest angle of the quadrilateral. largest angle of the triangle is 10° more than second largest angle of the triangle. what is the second largest angle of the triangle

Answer 1

Heya Friend ☺

let the ratio are 6x, 3x 4x and 5x

By using angle sum property of a quadrilateral

$6x + 3x + 4x + 5x = {360}^{0} \\ 18x = 360 \\ x = 20$
Now put the values of x in all the Angles
$6 \times 20 = {120}^{0} \\ 3 \times 20 = {60}^{0} \\ 4 \times 20 = {80}^{0} \\ 5 \times 20 = {100}^{0}$
According to question

Smallest angle of triangle is one fourth of the largest side of the quadrilateral
$smallest \: angle \: of \: the \: triangle \: = \frac{1}{4} \times 120 \\ = {30}^{0}$
Now let the the first largest angle of triangle is x +10

then the second largest angle of the triangle is x

and smallest angle is given above =30

Now by applying angle sum property of the triangle
$x + x + 10 + 30 = 180 \\ 2x + 40 = 180 \\ 2x = 180 - 40 = 140 \\ x = \frac{140}{2} = {70}^{0}$

so the second largest angle of the triangle is 70°

The required answer is 70°

Hence,. solved


Hope it helped you

@mayankstar364