Question

In rectangle ABCD, m∠EAB = 4x + 6, m∠DEC = 10 - 11y, and m∠EBC = 60. Find the values of x and y.

Answer 1

To find the values of x and y in rectangle ABCD, we can use the properties of rectangles and angles. By setting up and solving a system of equations, we find that x = 2 and y = -5.

Step-by-step explanation:

To find the values of x and y, we need to use the properties of rectangles and angles. In rectangle ABCD, opposite angles are congruent. Therefore, we have:

m∠EAB = m∠EDC

4x + 6 = 10 - 11y

Simplifying the equation gives:

4x + 11y = 4

We also know that m∠EBC = 60. Since opposite angles in a rectangle are congruent, we have:

m∠EBC = m∠EDC

60 = 10 - 11y

Simplifying the equation gives:

11y = -50

To find the values of x and y, we can solve these two equations simultaneously. Solving the system of equations give us the values of x = 2 and y = -5.

Answer 2

To find the values of x and y in the rectangle ABCD, we can use the fact that the sum of the angles in a rectangle is 360 degrees. By setting up equations based on the given information and using the properties of a rectangle, we can solve for x and y. The values of x and y are 6 and approximately -12.73, respectively.

Step-by-step explanation:

To find the values of x and y, we can use the fact that the sum of the angles in a rectangle is 360 degrees.

From the given information, we have:

m∠EAB = 4x + 6

m∠DEC = 10 - 11y

m∠EBC = 60

Since ABCD is a rectangle, we have:

m∠EAB + m∠DEC = 180° (opposite angles)

4x + 6 + 10 - 11y = 180

4x - 11y + 16 = 180

4x - 11y = 164

Also, m∠EAB + m∠EBC = 90° (adjacent angles)

4x + 6 + 60 = 90

4x + 66 = 90

4x = 24

x = 6

Substituting x = 6 into the first equation:

4(6) - 11y = 164

24 - 11y = 164

-11y = 140

y = -140/11

Therefore, the value of x is 6 and the value of y is approximately -12.73.