Final answer:
To find the values of x and y in the given rectangle, we need to use the properties of angles in a rectangle. By setting up equations and solving for x and y, we can find their values.
Step-by-step explanation:
To find the values of x and y in the rectangle ABCD, we can use the fact that the sum of all four angles in a rectangle is 360 degrees. We are given that m∠EAB = 4x+6, m∠DEC = 10-11y, and m∠EBC = 60 degrees.
1. First, we know that m∠EAB + m∠EBC = 180 degrees (opposite angles in a rectangle are congruent).
2. Using this information, we can write the equation: (4x+6) + 60 = 180. Solving for x, we get x = 28.
3. Next, we know that m∠EBC + m∠DEC = 180 degrees (adjacent angles in a rectangle are supplementary).
4. Using this information, we can write the equation: 60 + (10-11y) = 180. Solving for y, we get y = -11.
Therefore, the values of x and y in the rectangle ABCD are x = 28 and y = -11.
Learn more about Angles in a rectangle