Question

∠a = 8x + 78° ∠b = 2x + 114° solve for x and then find the measure of ∠b ∠b =

Explanation:

Step1: Assume vertical - angle relationship

Since vertical angles are equal, we set $\angle A=\angle B$. So, $8z + 78=2z+114$.

Step2: Solve for z

Subtract $2z$ from both sides: $8z-2z + 78=2z-2z + 114$, which simplifies to $6z+78 = 114$. Then subtract 78 from both sides: $6z+78 - 78=114 - 78$, getting $6z=36$. Divide both sides by 6: $z=\frac{36}{6}=6$.

Step3: Find the measure of $\angle B$

Substitute $z = 6$ into the expression for $\angle B$. $\angle B=2z + 114$. So, $\angle B=2\times6+114=12 + 114=126^{\circ}$.

Answer:

$126$