Question

for what values of the variables must abcd be a parallelogram?

(type whole numbers.)

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, \(x = 35\) (since \(\angle B=\angle D\) and \(\angle A=\angle C\) in parallelogram \(ABCD\)).

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary. So, \(x + y=180\). Substitute \(x = 35\) into the equation: \(35+y = 180\). Then \(y=180 - 35\).

Answer:

\(x = 35\), \(y = 145\)