Question

b. if m∠xyz = 10x - 15 and m∠zyw = 6x + 12, and m∠
c. if m∠pqr = x + 10, m∠rqs = 2x + 5, and m∠pqs = 69, find x.

Explanation:

Step1: Use angle - addition property

Since $\angle PQS=\angle PQR+\angle RQS$, we can substitute the given angle - measures into the equation. So, $(x + 10)+(2x + 5)=69$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side of the equation. $x+2x+10 + 5=69$ simplifies to $3x+15 = 69$.

Step3: Isolate the variable term

Subtract 15 from both sides of the equation: $3x+15−15=69−15$, which gives $3x=54$.

Step4: Solve for x

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

Answer:

$x = 18$