Angle addition postulate applied to triangle NSMP: m∠MSP = 40° (sum of angles in a triangle is 180°).
Based on the information given in the image and your question, we can see that we're dealing with a triangle formed by lines NS, SM, and PA. We're also given that m∠NSM = 100° and m∠SPA = 40° (the angle opposite to side PA is supplementary to the angle opposite to side SA).
We can use the angle addition postulate to solve for m∠MSP. This postulate states that the sum of the angles in a triangle is equal to 180°. So, we can write the equation:
m∠NSM + m∠MSP + m∠SPA = 180°
Substituting the values we know:
100° + m∠MSP + 40° = 180°
Combining like terms:
m/MSP + 140° = 180°
Subtracting 140° from both sides:
m∠MSP = 180° - 140°
Therefore, m∠MSP = 40°.
In short, the angle m∠MSP is 40° because it's the difference between the sum of the other two angles in the triangle (180°) and the values of those two angles (100° and 40°).