평행선과 각의 성질

문제

두 평행선 $l, m$이 한 직선 $k$와 만날 때, 그림과 같이 각이 주어져 있다. $\angle x$의 크기를 구하시오.

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

% Transversal line k \draw (-1,1) -- (2,-3) node[below left] {$k$};

% Define intersection points \path[name path=line_l] (-2,0) -- (3,0); \path[name path=line_m] (-2,-2) -- (3,-2); \path[name path=line_k] (-1,1) -- (2,-3);

\path [name intersections={of=line_l and line_k, by=P}]; \path [name intersections={of=line_m and line_k, by=Q}];

% Label for 130 degrees (upper-right angle at P)
ode at (P) [above right, xshift=0.1cm, yshift=0.1cm] {$130^\circ$}; % Label for x (lower-right angle at Q)
ode at (Q) [below right, xshift=0.1cm, yshift=-0.1cm] {$x$};

\end{tikzpicture} \end{center}