Final answer:
The largest angle in a quadrilateral with angles in the ratio 6:7:8:9 is 108 degrees. This is found by adding the angles, equating them to the sum of quadrilateral angles (360 degrees), and solving for the common ratio.
Step-by-step explanation:
To find the value of the largest angle in a quadrilateral whose angles are in the ratio 6:7:8:9, we first need to know that the sum of all angles in any quadrilateral is 360 degrees. Given the ratio, we can represent the angles as 6x, 7x, 8x, and 9x. Adding these together, we have:
6x + 7x + 8x + 9x = 30x
This sum must equal 360 degrees, so we set up the equation:
30x = 360
Solving for x gives us:
x = 360 / 30
x = 12
Therefore, the angles are 6x = 72 degrees, 7x = 84 degrees, 8x = 96 degrees, and 9x = 108 degrees. The largest angle is 9x, which is 108 degrees.