Question

solve for x.
work it out
not feeling ready yet? these can help:
transversals of parallel lines: find angle measures (81)
solve linear equations: mixed review (81)
lesson: transversals of parallel lines

Explanation:

Step1: Identify angle - relationship

Assume lines $DE$ and $FG$ are parallel and $BC$ is a transversal. Then, the angles $(124 - x)^{\circ}$ and $(8x + 43)^{\circ}$ are corresponding angles (or alternate - exterior/alternate - interior depending on the parallel - line properties), and they are equal. So, we set up the equation $124−x = 8x + 43$.

Step2: Solve the linear equation

Add $x$ to both sides of the equation: $124=8x + 43+x$.
Combine like terms: $124 = 9x+43$.
Subtract 43 from both sides: $124 - 43=9x$, which gives $81 = 9x$.
Divide both sides by 9: $x=\frac{81}{9}=9$.

Answer:

$9$