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 can write 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: Solve for $x$

Subtract 5 from both sides: $175−5=34x+5 - 5$, which gives $170 = 34x$. Then divide both sides by 34: $x=\frac{170}{34}=5$.

Answer:

$x = 5$