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 ( square ) degrees and the interior angle of ( y ) measures ( square ) degrees.

check answer remaining attempts : 3

Explanation:

Step1: Use the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary (their sum is \( 180^{\circ}\)). Angle \( X\) and angle \( W\) are consecutive angles.
Let the measure of angle \( W\) be \( w\). We know that \( \angle X = 35^{\circ}\), and \( \angle X+\angle W=180^{\circ}\).
So, \( w = 180 - 35\).

Step2: Calculate the value of \( w\)

\( w=145^{\circ}\).
Since in a parallelogram, opposite angles are equal. Angle \( Y\) is opposite to angle \( W\). So, \( \angle Y=\angle W = 145^{\circ}\).

Answer:

The interior angle of \( W \) measures \( 145 \) degrees and the interior angle of \( Y \) measures \( 145 \) degrees.