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
Hi,
We do not allow outside interference with our homework questions. Please refrain from doing so in the future.
Thank you.
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.