Question

in parallelogram w x y z, the interior angle at point y measures 75 degrees. what is the measure of the interior angle at point x?

Explanation:

Step1: Recall the property of a parallelogram

In a parallelogram, consecutive angles are supplementary. That is, the sum of consecutive angles is \(180^{\circ}\).

Step2: Identify the relationship between angles at \(Y\) and \(X\)

Angle at \(Y\) and angle at \(X\) are consecutive angles in parallelogram \(WXYZ\). Let the measure of the angle at \(Y\) be \(y = 75^{\circ}\) and the measure of the angle at \(X\) be \(x\). Then \(x + y=180^{\circ}\).

Step3: Solve for \(x\)

Substitute \(y = 75^{\circ}\) into the equation \(x + y=180^{\circ}\). We get \(x=180^{\circ}-75^{\circ}\).

$$x = 105^{\circ}$$

Answer:

\(105\) degrees