Let's find the value of each variable one at a time.
Value of x
The angles that measure 2x + 41 and 115 are opposite angles. Recall the Theorem 6.4, which tells us that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore, the measures of these angles are equal.
2x + 41= 115
Let's solve above equation to find the value of x.
The sides with lengths 2y + 19 and 3y + 13 are opposite sides in our parallelogram. Recall the Theorem 6.3, which tells us that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore, the lengths of the opposite sides are equal.
2y + 19= 3y + 13
Let's solve above equation to find the value of y.
