Question

∠a = 8x + 74°, ∠b = 2x + 56°. solve for x and then find the measure of ∠b. ∠b =

Explanation:

Step1: Assume angles are supplementary

Since the two angles $\angle A$ and $\angle B$ are likely supplementary (adjacent - linear pair), we set up the equation $\angle A+\angle B = 180^{\circ}$. So, $(8x + 74)+(2x+56)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(8x+2x)+(74 + 56)=180$, which simplifies to $10x+130 = 180$.

Step3: Isolate the variable term

Subtract 130 from both sides of the equation: $10x+130-130=180 - 130$, resulting in $10x=50$.

Step4: Solve for $x$

Divide both sides by 10: $\frac{10x}{10}=\frac{50}{10}$, so $x = 5$.

Step5: Find the measure of $\angle B$

Substitute $x = 5$ into the expression for $\angle B$. $\angle B=2x + 56$. Then $\angle B=2\times5+56$.
$\angle B=10 + 56=66^{\circ}$.

Answer:

$66$