Question

The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?
A) 80 degrees
B) 60 degrees
C) 120 degrees
D) 40 degrees

Answer 1

$\bf\huge\color{red}{SOLUTION;}$

Given the angles of a quadrilateral are in the ratio of 2:4:7:5
Let the angles of a quadrilateral are 2x, 4x, 7x, 5x
But we know that sum of the angles = 360 degrees.
=> 2x + 4x + 7x + 5x = 360
=> x = 20
Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.
One of the angle of the triangle = 2 x 40 = 80 degrees
The other angle is 180 - (40 + 80) = 60 degrees.

Hence the second largest angle of the triangle is 60 degrees.

Answer 2

Answer:

The correct answer is option (B) 60 degrees

Step-by-step explanation:

Given,

The angles of a quadrilateral are in the ratio 2:4:7:5

The smallest angle of the quadrilateral is equal to the smallest angle of the triangle

One of the angles of the triangles is twice the smallest angle

To find,

The second largest angle of the triangle

Solution

Since the angles of a quadrilateral are in the ratio 2:4:7:5 we have,

the four angles of the quadrilateral are 2x, 4x, 7x and 5x

We know the sum of four angles of a quadrilateral = 360 we have

2x+4x+7x+5x = 360

18x = 360

x  = $\frac{360}{18}$ = 20

Hence the four angles of the quadrilateral are 40,80,140,100

The smallest angle of the quadrilateral = 40

Since it is given that the  smallest angle of the quadrilateral is equal to the smallest angle of the triangle,

The smallest angle of the triangle = 40

Also, one of the angles of the triangle is twice the smallest angle of the triangle

One of the three angles of the triangle = 2×40 = 80

Let 'y' be the third angle of the triangle.

Since the sum of three angles of a triangle is 180 we have,

40+80+x = 180

120+x = 180

x = 180 -120 = 60

Hence the three angles of the triangle are 40,60,80.

∴ The second largest angle of the triangle = 60degrees

Hence the correct answer is option (B)

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