Question

three angles of quadrilateral are in the ratio 2:3:7.the mean of these angles is 64degree.find the fourth angle

Answer 1

the fourth angle is 168 degrees

Answer 2

Given: Three angles of a quadrilateral are in the ratio 2:3:7 and the mean of these angles is 64degree.

To find: We have to find the fourth angle.

Solution:

The three angles of the quadrilateral are in the ratio of 2:3:7.

Let the angles be 2x, 3x and 7x.

The mean of the three angles is (2x+3x+7x)/3=4x.

This mean of the angles is equal to 64°.

So, we can write-

$4x = 64 \\ x = 16$

Thus, the value of x is 16.

Now we know that sum of four angles of a quadrilateral is 360°.

Let the fourth angle be y.

So, we can write-

$12x + y = 360 \\ 12 \times 16 + y = 360 \\ y = 360 - 192 \\ y = 168$

Thus, the fourth angle of the quadrilateral is 168°.