Question

∠a=(4x + 4)°
∠g=(10x + 8)°
establish an equation that represents the relationship in the diagram.
solve the equation for the variable.
what are the measures of ∠a and ∠g?

Explanation:

Step1: Identify angle - relationship

Assume the two lines are parallel and the two angles are corresponding (or alternate - interior/exterior depending on the actual parallel - line setup), so $\angle A=\angle G$. The equation is $4x + 4=10x+8$.

Step2: Solve the equation for $x$

Subtract $4x$ from both sides:
$4 = 10x+8 - 4x$, which simplifies to $4 = 6x+8$.
Then subtract 8 from both sides: $4 - 8=6x$, so $- 4 = 6x$.
Divide both sides by 6: $x=-\frac{4}{6}=-\frac{2}{3}$.

Step3: Find the measure of $\angle A$

Substitute $x =-\frac{2}{3}$ into the expression for $\angle A$:
$\angle A=4x + 4=4\times(-\frac{2}{3})+4=\frac{-8 + 12}{3}=\frac{4}{3}=1\frac{1}{3}$ degrees.

Step4: Find the measure of $\angle G$

Since $\angle A=\angle G$, $\angle G=\frac{4}{3}=1\frac{1}{3}$ degrees.

Answer:

The equation is $4x + 4=10x+8$, $x =-\frac{2}{3}$, $\angle A=\frac{4}{3}$ degrees, $\angle G=\frac{4}{3}$ degrees.