## Geometry: Common Core (15th Edition)

$x = 1$
Theorem 6-20 states that in an isosceles trapezoid, diagonals are congruent. Let's set the two diagonals equal to one another: $QS = RP$ Let's plug in the expressions for each diagonal: $x + 5 = 3x + 3$ Subtract $5$ from each side of the equation to move constants to the right side of the equation: $x = 3x - 2$ Subtract $3x$ from each side of the equation to move the variable to the left side of the equation: $-2x = -2$ Divide each side by $-2$ to solve for $x$: $x = 1$