Question 28
Let $ABC$ be an isosceles triangle with $AB = AC$ and let $n \gt 1$ be an integer. Point $M$ lies on the line segment $AB$ such that $nAM = AB$. Consider the points $P_1, P_2, \dots, P_{n-1}$ on the side $BC$ with $BP_1 = P_1P_2 = P_2P_3 = \dots = P_{n-1}C = \frac{1}{n}BC$. Prove that
$$
\angle MP_1A + \angle MP_2A + \dots + \angle MP_{n-1}A = \frac{1}{2} \angle BAC.
$$
$$
\angle MP_1A + \angle MP_2A + \dots + \angle MP_{n-1}A = \frac{1}{2} \angle BAC.
$$