평행선과 각의 관계

문제

오른쪽 그림에서 두 직선 $l$과 $m$은 서로 평행할 때, $\angle x$의 크기는?

\begin{center} \begin{tikzpicture} % Parallel lines l and m \draw[thick] (-3,0) -- (3,0) node[right] {$l$}; \draw[thick] (-3,-2) -- (3,-2) node[right] {$m$};

% Transversal line k \draw[thick] (-2,2) -- (2,-3) node[below] {$k$};

% Points for labeling angles \coordinate (L1) at (-3,0); % Point on l to the left \coordinate (L_INT) at (-0.5,0); % Intersection on l \coordinate (L2) at (3,0); % Point on l to the right

\coordinate (M1) at (-3,-2); % Point on m to the left \coordinate (M_INT) at (1.5,-2); % Intersection on m \coordinate (M2) at (3,-2); % Point on m to the right

\coordinate (K_TOP) at (-2,2); % Point on k above l \coordinate (K_BOT) at (2,-3); % Point on k below m

% Mark the 130 degree angle (top-left exterior at L_INT) \draw pic[draw, angle radius=8mm, "{$130^\circ$}", angle eccentricity=1.3] {angle = L1--L_INT--K_TOP};

% Mark angle x (bottom-right interior at M_INT) \draw pic[draw, angle radius=8mm, "{$x$}"] {angle = M2--M_INT--K_BOT}; \end{tikzpicture} \end{center}