Question

if \\(\overline{pq} \cong \overline{ps}\\), \\(m\angle prq = v + 52^\circ\\), and \\(m\angle prs = 3v\\), what is \\(m\angle qrs\\)?
\\(m\angle qrs = \square^\circ\\)

Explanation:

Step1: Identify angle relationship

$\angle PRQ$ and $\angle PRS$ are congruent, so $v + 52 = 3v$

Step2: Solve for $v$

$3v - v = 52$
$2v = 52$
$v = 26$

Step3: Calculate $\angle PRS$

$m\angle PRS = 3v = 3\times26 = 78^\circ$

Step4: Find $\angle QRS$

$\angle QRS = \angle PRS + \angle PRQ = 78^\circ + 78^\circ = 156^\circ$

Answer:

$156$