Let θ_1 be the angle between two lines 2 x+3 y+ c_1=0 and -x+5 y+ c_2=0, and θ_2 be the angle between two lines; 2 x+3 y+ c_1=0 and -x+5 y+ c_3=0,…

Let $\displaystyle \theta_1$ be the angle between two lines $$\begin{aligned} & 2 x+3 y+\mathrm{c}_1=0 \text { and }-x+5 y+\mathrm{c}_2=0, \text { and } \\ & \theta_2 \text { be the angle between two lines } \\ & 2 x+3 y+\mathrm{c}_1=0 \text { and }-x+5 y+\mathrm{c}_3=0, \end{aligned} $$ where $\displaystyle \mathrm{c}_1, \mathrm{c}_2, \mathrm{c}_3$ are any real numbers : Statement $\displaystyle 1$: If $\displaystyle c_2$ and $\displaystyle c_3$ are proportional, then $\displaystyle \theta_1=\theta_2$.Statement $\displaystyle 2$ : $\displaystyle \theta_1=\theta_2$ for all $\displaystyle c_2$ and $\displaystyle c_3$.