Question

p
$(4x + 15)^{circ}$
q
r
s
$(10x - 3)^{circ}$
t
a) $59^{circ}$
disappointed
exhausted
shocked
outraged
overwhelmed
b) $61^{circ}$
c) $63^{circ}$
d) $117^{circ}$
e) $119^{circ}$
© gina wilson (all things algebra

Explanation:

Step1: Set up the equation

Since \( \angle PQS\) and \( \angle RQT\) are vertical angles, they are equal. But we can also use the fact that \( \angle PQS\) and \( \angle SQT\) are supplementary (they form a linear - pair). So \(4x + 15+10x - 3=180\).
Combine like terms: \(14x+12 = 180\).

Step2: Solve for \(x\)

Subtract 12 from both sides: \(14x=180 - 12\), so \(14x=168\).
Divide both sides by 14: \(x=\frac{168}{14}=12\).

Step3: Find the measure of \( \angle PQS\)

Substitute \(x = 12\) into \(4x + 15\).
\(4x+15=4\times12 + 15\).
First, calculate \(4\times12=48\), then \(48+15 = 63\).

Answer:

C. \(63^{\circ}\)