Line R T and line S U slightly inclined with horizontal intersects at V. The upward and downward angles of the intersecting lines are obtuse. The left and right angles of the intersecting lines are acute. The measure of angle R V U is labeled as left parenthesis 8 y minus 33 right parenthesis degrees. The measure of angle S V T is labeled as left parenthesis 5 y plus 9 right parenthesis degrees.

Given the description, it sounds like angle RVU and angle SVT are vertical angles. With this known, the angles are equivalent and the two equations can be set equal to each other.

5y+9=8y-33 vertical angles are congruent

-5y - 5y

9 = 3y - 33 Use inverse operations to move all variables to one side of the equation

+33 + 33 Add 33 to both sides of the equation to isolate the variable

42=3y

/3 / 3 Divide both sides by 3 in order to isolate the variable

14 = y Once simplified, the variable y is equal to 14

In order to find the measure of the angle, the value of the variable needs to be substituted back into one of the equations.

5y+9

5 (14) + 9

70 + 9

79

The measure of angle RVU and angle SVT is 79 degrees