Question

use the following diagram and the angle addition postulate to solve for the value of x.
if m∠xyz = 10x - 15 and m∠zyw = 6x + 12, and m∠xyw = 99, find x.
if m∠pqr = x + 10, m∠rqs = 2x + 5, and m∠pqs = 69, find x.

Explanation:

Step1: Apply angle - addition postulate

According to the angle - addition postulate, if an angle $\angle PQS$ is composed of $\angle PQR$ and $\angle RQS$, then $m\angle PQS=m\angle PQR + m\angle RQS$. Given $m\angle PQR=x + 10$, $m\angle RQS=2x + 5$, and $m\angle PQS = 69$, we have the equation $(x + 10)+(2x + 5)=69$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x+10 + 5=69$, which simplifies to $3x+15 = 69$.

Step3: Isolate the variable term

Subtract 15 from both sides of the equation: $3x+15-15=69 - 15$, resulting in $3x=54$.

Step4: Solve for x

Divide both sides of the equation by 3: $\frac{3x}{3}=\frac{54}{3}$, so $x = 18$.

Answer:

$x = 18$