The ratio of three consecutive angles in a cyclic quadrilateral is 2:3:4. Find the largest angle of the quadrilateral, in degrees.

Since opposite angles are supplementary, we have

2x+4x = 180
x = 30
and the angles are 60,90,120,90

60&120

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2x+4x=180

6x=180
X=30

To find the largest angle of the cyclic quadrilateral, we need to use the fact that the opposite angles in a cyclic quadrilateral sum up to 180 degrees.

Let's assume the three consecutive angles in the ratio 2:3:4 are x, y, and z respectively.

According to the given ratio, we have:

x : y : z = 2 : 3 : 4

We can express these ratios in terms of a common variable. Let's assume the common variable is a:

x = 2a
y = 3a
z = 4a

Now, since the opposite angles in a cyclic quadrilateral sum up to 180 degrees, we know that:

x + z = 180

Substituting the values of x and z, we have:

2a + 4a = 180
6a = 180
a = 30

Now, we can find the values of x, y, and z:

x = 2a = 2 * 30 = 60
y = 3a = 3 * 30 = 90
z = 4a = 4 * 30 = 120

Therefore, the largest angle of the quadrilateral is 120 degrees.