1. The problem asks us to form an equation using the given angle measures of a parallelogram and then find the numerical values of each angle. 2. Important property: In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180 degrees). 3. Given angles are $x+40^\circ$ and $3x-20^\circ$ which are adjacent angles. 4. Since adjacent angles are supplementary, we write the equation: $$ (x+40) + (3x-20) = 180 $$ 5. Simplify the equation: $$ x + 40 + 3x - 20 = 180 $$ $$ 4x + 20 = 180 $$ 6. Subtract 20 from both sides: $$ 4x = 160 $$ 7. Divide both sides by 4: $$ x = 40 $$ 8. Substitute $x=40$ back into the angle expressions: - First angle: $x + 40 = 40 + 40 = 80^\circ$ - Second angle: $3x - 20 = 3(40) - 20 = 120 - 20 = 100^\circ$ 9. Opposite angles are equal, so the parallelogram's angles are $80^\circ$, $100^\circ$, $80^\circ$, and $100^\circ$. Final answer: The angles of the parallelogram are $80^\circ$ and $100^\circ$.