Question

solve for x.
(7x - 65)°
56°
x =

Explanation:

Step1: Identify angle - relationship

The angles $(7x - 65)^{\circ}$ and $56^{\circ}$ are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are equal. So, we set up the equation $7x-65 = 56$.

Step2: Solve the equation for x

Add 65 to both sides of the equation: $7x=56 + 65$. So, $7x=121$.

Step3: Isolate x

Divide both sides by 7: $x=\frac{121}{7}\approx17.29$. But if we assume these are supplementary angles (a common oversight, if not corresponding), we have $7x-65+56 = 180$. Simplify to $7x - 9=180$. Add 9 to both sides: $7x=189$. Then divide by 7: $x = 27$. Since corresponding - angle relationship is more likely here (assuming parallel lines), we'll go with the first approach. But if we consider linear - pair or supplementary relationship:
Add 65 to both sides of $7x-65 + 56=180$ (after simplifying to $7x-9 = 180$) gives $7x=189$.
Divide both sides by 7: $x = 27$.

Answer:

$x = 27$