Question

converse parallelogram proofs practice
complete this assessment to review what youve learned. it will not count toward your grade.
in parallelogram wxyz, the interior angle of x measures 35 degrees and the interior angle of z also measures 35 degrees. what are the interior angle measures of w and y? (1 point)
the interior angle of w measures degrees and the interior angle of y measures degrees

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - angles are equal and adjacent - angles are supplementary (sum to 180 degrees).

Step2: Identify opposite and adjacent angles

Angle \(X\) and angle \(Z\) are opposite angles. Angle \(W\) is adjacent to angle \(X\), and angle \(Y\) is adjacent to angle \(Z\).

Step3: Calculate angle \(W\)

Since angle \(W\) and angle \(X\) are adjacent, and the sum of adjacent angles in a parallelogram is 180 degrees. Let the measure of angle \(W\) be \(w\). Then \(w + 35=180\), so \(w = 180 - 35=145\) degrees.

Step4: Calculate angle \(Y\)

Since angle \(Y\) and angle \(Z\) are adjacent, and the sum of adjacent angles in a parallelogram is 180 degrees. Let the measure of angle \(Y\) be \(y\). Then \(y + 35=180\), so \(y = 180 - 35 = 145\) degrees.

Answer:

145, 145