1. The problem gives two parallel lines IJ and KL crossed by a transversal GH, with angles at points M and N: (7x - 65)° and 56° respectively. 2. Since IJ and KL are parallel, angles at M and N on the same side of the transversal are corresponding angles and thus equal. 3. Set the expressions equal: $$7x - 65 = 56$$ 4. Solve for $x$: add 65 to both sides: $$7x = 56 + 65 = 121$$ 5. Divide both sides by 7: $$x = \frac{121}{7} = 17.2857$$ 6. Therefore, the value of $x$ is approximately $17.29$.