Question

∠a = 8x - 8°, ∠b = 5x + 25°. solve for x and then find the measure of ∠b: ∠b = °

Explanation:

Step1: Identify angle - relationship

Since the two angles are corresponding angles and the lines are parallel, $\angle A=\angle B$. So, $8x - 8=5x + 25$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $8x-5x - 8=5x-5x + 25$, which simplifies to $3x-8 = 25$. Then add 8 to both sides: $3x-8 + 8=25 + 8$, getting $3x=33$. Divide both sides by 3: $x=\frac{33}{3}=11$.

Step3: Find the measure of $\angle B$

Substitute $x = 11$ into the expression for $\angle B$. $\angle B=5x + 25=5\times11+25=55 + 25=80^{\circ}$.

Answer:

$80$