Question

1. $mangle vut = 175^{circ}$, $mangle vuj = 17x - 3$, and $mangle jut = 17x + 8$. find $x$.

Explanation:

Step1: Use angle - addition postulate

Since $\angle VUT=\angle VUJ+\angle JUT$, we have the equation $175=(17x - 3)+(17x + 8)$.

Step2: Simplify the right - hand side of the equation

Combine like terms: $(17x-3)+(17x + 8)=17x+17x-3 + 8=34x+5$. So the equation becomes $175 = 34x+5$.

Step3: Isolate the variable term

Subtract 5 from both sides of the equation: $175-5=34x+5 - 5$, which simplifies to $170 = 34x$.

Step4: Solve for x

Divide both sides of the equation by 34: $\frac{170}{34}=x$. So $x = 5$.

Answer:

$x = 5$