평행선과 꺾인 선의 각도 구하기

문제

다음 그림에서 두 직선 $l$과 $m$이 평행할 때, $\angle x$의 크기를 구하시오.

[ \begin{tikzpicture} \path (0,2) coordinate (L1) (5,2) coordinate (L2); \path (0,0) coordinate (M1) (5,0) coordinate (M2);

\draw[black, thick] (L1) -- (L2) node[right] {$l$}; \draw[black, thick] (M1) -- (M2) node[right] {$m$};

\coordinate (A) at (1,2); \coordinate (B) at (4,0); \coordinate (P) at (2.5,1.2);

\draw[black, thick] (A) -- (P) -- (B);

% Points for angle markings \coordinate (A_left) at (0.5,2); % Point on l to the left of A \coordinate (B_right) at (4.5,0); % Point on m to the right of B

% Angles \pic [draw, "$55^\circ$", angle eccentricity=1.2] {angle = P--A--A_left}; % Angle at A \pic [draw, "$30^\circ$", angle eccentricity=1.2] {angle = B_right--B--P}; % Angle at B \pic [draw, "$x$", angle eccentricity=1.2] {angle = A--P--B}; % Angle at P

\node[above] at (A) {$A$}; \node[below] at (B) {$B$}; \node[above right] at (P) {$P$}; \end{tikzpicture} ]