Question

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

x = 35

y = 145

(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 \(\angle A\) and \(\angle C\) are opposite angles and \(x\) is given as equal to the measure of \(\angle A\) which is \(35^{\circ}\)).

Step2: Use the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary (\(x+(y - 30)=180\)). Substitute \(x = 35\) into the equation: \(35+(y - 30)=180\).
Simplify the left - hand side: \(35+y-30=y + 5\).
So, \(y+5=180\).
Subtract 5 from both sides: \(y=180 - 5=175\).

Answer:

\(x = 35\), \(y = 175\)