Question

for what values of the variables must abcd be a parallelogram?
x =
y =
(type whole numbers.)
(image of parallelogram abcd with angles: b: 3x°, a: 3y°, c: (y + 74)°, d: (4x - 23)°)

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, \(3x=4x - 23\) and \(3y=y + 74\).

Step2: Solve the equation for \(x\)

For \(3x=4x - 23\), subtract \(3x\) from both sides:
\(0=x - 23\), then \(x = 23+0=27\)

Step3: Solve the equation for \(y\)

For \(3y=y + 74\), subtract \(y\) from both sides:
\(2y=74\), then \(y=\frac{74}{2}=29\)

Answer:

\(x = 27\), \(y = 29\)