Question

if m∠4 is 5(x + 1) degrees and m∠5 is - 5x - 25 degrees, what is x?

Explanation:

Step1: Set up the equation

Assume that $\angle4$ and $\angle5$ are either vertical - angles (equal) or supplementary (sum to 180 degrees). Since they are a linear - pair of angles, $m\angle4 + m\angle5=180$. So, $5(x + 1)+(-5x - 25)=180$.

Step2: Expand the first term

Expand $5(x + 1)$ using the distributive property $a(b + c)=ab+ac$. We get $5x+5+(-5x - 25)=180$.

Step3: Combine like terms

$(5x-5x)+(5 - 25)=180$. Simplifying the left - hand side gives $0x-20 = 180$, or $-20=180$, which is incorrect. Let's assume they are vertical angles. If $\angle4$ and $\angle5$ are vertical angles, then $m\angle4=m\angle5$. So, $5(x + 1)=-5x - 25$.

Step4: Expand the left - hand side

Using the distributive property, we have $5x+5=-5x - 25$.

Step5: Add $5x$ to both sides

$(5x + 5x)+5=( - 5x+5x)-25$, which simplifies to $10x+5=-25$.

Step6: Subtract 5 from both sides

$10x+(5 - 5)=-25 - 5$. So, $10x=-30$.

Step7: Solve for $x$

Divide both sides by 10: $x=\frac{-30}{10}=-3$.

Answer:

$x=-3$