The angle between the line joining the points $\left(1,-2\right),\left(3,2\right)$  and the line $x+2y-7=0$ is

Slope $=\frac{y_2-y_1}{x_2-x_1}$

$m_1=\frac{2+2}{3-1}$

$=\frac{4}{2}$  $=2$

Slope $e\left(m_2\right)=\frac{-a}{b}=\frac{-1}{2}$

$m_1.m_2=2\times \frac{-1}{2}=-1$

$\therefore$  product of the slopes of two lines is $-1$

$\therefore$  Two lines are perpendicular to each other.

$\therefore$  Angle between two lines is $90°=\frac{\pi }{2}$