Question

geometry > d.5 transversals of parallel lines: solve for x, igv
solve for x.
(3x + 9)°
(7x + 21)°
x =
submit

Explanation:

Step1: Identify angle - relationship

Since $DE\parallel FG$, the angles $(3x + 9)^{\circ}$ and $(7x+21)^{\circ}$ are same - side interior angles. Same - side interior angles of parallel lines are supplementary, so $(3x + 9)+(7x + 21)=180$.

Step2: Simplify the left - hand side

Combine like terms: $(3x+7x)+(9 + 21)=180$, which gives $10x+30 = 180$.

Step3: Isolate the variable term

Subtract 30 from both sides: $10x+30-30=180 - 30$, resulting in $10x=150$.

Step4: Solve for x

Divide both sides by 10: $\frac{10x}{10}=\frac{150}{10}$, so $x = 15$.

Answer:

$15$