Let's assume the measures of the angles are 1x, 3x, 7x, and 9x, where x is a common multiplier for the ratio. The sum of the angles in a quadrilateral is always 360 degrees. So, we can set up an equation:
1x + 3x + 7x + 9x = 360
Combine like terms:
20x = 360
Now, solve for x:
x = 360 / 20
x = 18
Now that we have the value of x, we can find the measures of all angles:
1x = 1 * 18 = 18 degrees
3x = 3 * 18 = 54 degrees
7x = 7 * 18 = 126 degrees
9x = 9 * 18 = 162 degrees
So, the angles of the quadrilateral are 18 degrees, 54 degrees, 126 degrees, and 162 degrees.
Answers & Comments
Let's assume the measures of the angles are 1x, 3x, 7x, and 9x, where x is a common multiplier for the ratio. The sum of the angles in a quadrilateral is always 360 degrees. So, we can set up an equation:
1x + 3x + 7x + 9x = 360
Combine like terms:
20x = 360
Now, solve for x:
x = 360 / 20
x = 18
Now that we have the value of x, we can find the measures of all angles:
1x = 1 * 18 = 18 degrees
3x = 3 * 18 = 54 degrees
7x = 7 * 18 = 126 degrees
9x = 9 * 18 = 162 degrees
So, the angles of the quadrilateral are 18 degrees, 54 degrees, 126 degrees, and 162 degrees.