I'm solving a problem (about circles and geometric fiqures), during a project I came up with this system, and in contains all my work, I'm not be able to solve it further so I need some help.
$$ \begin{cases} \theta_3+\theta_5+\theta_8+\theta_{11}+\theta_{13}=360\\ \theta_1+\theta_2+\theta_3=180\\ \theta_4+\theta_5+\theta_6=180\\ \theta_7+\theta_8+\theta_9=180\\ \theta_{10}+\theta_{11}+\theta_{12}=180\\ \theta_{13}+\theta_{14}+\theta_{15}=180\\ \theta_8+\theta_{11}+\theta_{13}=180\\ \theta_5+\theta_8+\theta_{11}=180\\ \theta_3+\theta_{13}=180\\ \theta_3+\theta_5=180\\ 2\theta_1+\theta_3=180\\ 2\theta_7+\theta_8=180\\ 2\theta_8+\theta_{13}=180\\ \theta_9+\theta_{10}=2\theta_8\\ \theta_3=2\theta_4\\ \theta_5=2\theta_1\\ \theta_1+\theta_4=90\\ \theta_2+\theta_{15}=90\\ \theta_9+\theta_{10}=\theta_8+\theta_{11}\\ \theta_3=\theta_8+\theta_{11}\\ \theta_7=\theta_{12}\\ \theta_5=\theta_{13}\\ \theta_6=\theta_{14}\\ \theta_4=\theta_{15}\\ \theta_1=\theta_2\\ \theta_7=\theta_9\\ \theta_8=\theta_{11} \end{cases} $$
Thanks fo any help.
I plugged your equations in a matrix calculator and got:
$$ \theta_{1}=\theta_{2}=30,\\ \theta_{3}=120,\\ \theta_{4}=\theta_{5}=\theta_{6}=\theta_{7}=\theta_{8}=\theta_{9}=\theta_{10}=\theta_{11}=\theta_{12}=\theta_{13}=\theta_{14}=\theta_{15}=60. $$