Question

if m∠nsm = 82°, then what is m∠psm?

Explanation:

Step1: Identify vertical - angle relationship

$\angle NSM$ and $\angle PSK$ are vertical angles, so $\angle PSK=\angle NSM = 82^{\circ}$

Step2: Use linear - pair relationship

$\angle PSK$ and $\angle PSM$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, we have $\angle PSM=180^{\circ}-\angle PSK$

Step3: Calculate $\angle PSM$

$\angle PSM = 180^{\circ}-82^{\circ}=98^{\circ}$

Answer:

$98^{\circ}$