Question

∠a = 8x + 6°, ∠b = 4x + 38°. solve for x and then find the measure of ∠b: ∠b =

Explanation:

Step1: Identify angle - relationship

Assume $\angle A$ and $\angle B$ are corresponding angles (since lines are parallel as indicated by arrow - heads), so $\angle A=\angle B$.
$8x + 6=4x+38$

Step2: Solve for $x$

Subtract $4x$ from both sides:
$8x-4x + 6=4x-4x+38$
$4x+6 = 38$
Subtract 6 from both sides:
$4x+6 - 6=38 - 6$
$4x=32$
Divide both sides by 4:
$x=\frac{32}{4}=8$

Step3: Find the measure of $\angle B$

Substitute $x = 8$ into the expression for $\angle B$.
$\angle B=4x + 38$
$\angle B=4\times8+38$
$\angle B=32 + 38$
$\angle B = 70^{\circ}$

Answer:

$70$