Final answer:
The value of x in quadrilateral ABCD, with m∣A = 80, m∣B = 2x, m∣C = x, and m∣D = 4x, is 40. This was determined by adding up the angles and setting them equal to 360 degrees, then solving for x.
Step-by-step explanation:
To find the value of x in quadrilateral ABCD, we can use the fact that the sum of interior angles in any quadrilateral is 360 degrees. Given m∣A = 80, m∣B = 2x, m∣C = x, and m∣D = 4x, we can set up the following equation:
80 + 2x + x + 4x = 360
Combining like terms, we get:
7x + 80 = 360
Subtract 80 from both sides to isolate the term with x:
7x = 280
Divide both sides by 7 to solve for x:
x = 40
Therefore, the value of x is 40.