Let's find the value of each variable one at a time.
Value of y
Notice that the angles that measure 106 and 3y+19 are opposite angles. Recall the Parallelogram Opposite Angles Theorem says that if a quadrilateral is a parallelogram, then its opposite angles are congruent. Therefore, for the figure to be a parallelogram, the measures of these angles must be equal.
106=3y+19
Let's solve the above equation.
Notice that the sides with lengths x+11 and 2x+9 are opposite sides in our quadrilateral. Recall the Parallelogram Opposite Sides Theorem says that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore, the lengths of the opposite sides must be equal.
x+11=2x+9
Let's solve the equation.
