Question

b. if m∠xyz = 10x - 15 and m∠zyw = 6x + 12, and m∠xyw = 99, find x.

Explanation:

Step1: Use angle - addition postulate

Since $\angle XYZ+\angle ZYW = \angle XYW$, we substitute the given angle - measures. So, $(10x - 15)+(6x + 12)=99$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side. $(10x+6x)+(-15 + 12)=99$, which simplifies to $16x-3 = 99$.

Step3: Add 3 to both sides

To isolate the term with $x$, we add 3 to both sides of the equation. $16x-3 + 3=99 + 3$, resulting in $16x=102$.

Step4: Solve for x

Divide both sides by 16. $x=\frac{102}{16}=\frac{51}{8}=6.375$.

Answer:

$x = 6.375$