Question

1. ∠w and ∠v are supplementary. ∠w is 10 degrees more than four times as big as ∠v. how big is each angle? m∠w = ____ m∠v = ____

Explanation:

Step1: Set up equations

Let $m\angle V = x$. Then $m\angle W=4x + 10$. Since $\angle W$ and $\angle V$ are supplementary, $m\angle W+m\angle V = 180$. So, $(4x + 10)+x=180$.

Step2: Simplify the equation

Combine like - terms: $4x+x+10 = 180$, which gives $5x+10 = 180$.

Step3: Solve for $x$

Subtract 10 from both sides: $5x=180 - 10=170$. Then divide both sides by 5: $x=\frac{170}{5}=34$.

Step4: Find $m\angle W$

Substitute $x = 34$ into the expression for $m\angle W$: $m\angle W=4x + 10=4\times34+10=136 + 10=146$.

Answer:

$m\angle W = 146^{\circ}$, $m\angle V=34^{\circ}$