Question

type the correct answer in each box. spell all words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s). in each system, lines wx and yz are parallel. identify an angle which is supplementary to angle m. then, determine the measure of the supplementary angle. \

$$\begin{tabular}{|c|c|c|} \\hline system & angle supplementary to angle m & measure of angle supplementary to angle m \\\\ \\hline \\begin{tikzpicture}scale=0.6 \\draw-> (0,0) -- (0,5) nodeabove {}; \\draw-> (-2,3) -- (2,1) noderight {x}; \\draw-> (-2,2) -- (2,0) noderight {z}; \\filldraw (-1,4) circle (2pt) nodeabove {w}; \\filldraw (-1,3) circle (2pt) nodeleft {a}; \\filldraw (-1,2.5) circle (2pt) nodeleft {d}; \\filldraw (-1,2) circle (2pt) nodeleft {b}; \\filldraw (-1,1.5) circle (2pt) nodeleft {c}; \\filldraw (-1,1) circle (2pt) nodeleft {g}; \\filldraw (-1,0.5) circle (2pt) nodeleft {e}; \\filldraw (-1,0) circle (2pt) nodeleft {f}; \\filldraw (-1,-0.5) circle (2pt) nodeleft {m}; \\filldraw (1,0) circle (2pt) noderight {z}; \ ode at (-1,-1) {$m\\angle m = 45^\\circ$}; \\end{tikzpicture} & angle \\boxed{} & \\boxed{} $^\\circ$ \\\\ \\hline \\begin{tikzpicture}scale=0.6 \\draw-> (-2,2) -- (2,4) noderight {y}; \\draw-> (-2,1) -- (2,3) noderight {w}; \\draw-> (-2,0) -- (2,2) noderight {}; \\draw-> (-2,-1) -- (2,1) noderight {z}; \\filldraw (-1,3) circle (2pt) nodeabove {w}; \\filldraw (-1,2.5) circle (2pt) nodeleft {h}; \\filldraw (-1,2) circle (2pt) nodeleft {k}; \\filldraw (-1,1.5) circle (2pt) nodeleft {m}; \\filldraw (-1,1) circle (2pt) nodeleft {j}; \\filldraw (-1,0.5) circle (2pt) nodeleft {x}; \\filldraw (1,2) circle (2pt) noderight {y}; \\filldraw (1,1.5) circle (2pt) noderight {p}; \\filldraw (1,1) circle (2pt) noderight {q}; \\filldraw (1,0.5) circle (2pt) noderight {s}; \\filldraw (1,0) circle (2pt) noderight {r}; \\filldraw (1,-0.5) circle (2pt) noderight {z}; \ ode at (-1,-1) {$m\\angle m = 75^\\circ$}; \\end{tikzpicture} & angle \\boxed{} & \\boxed{} $^\\circ$ \\\\ \\hline \\end{tabular}$$

note: figures are not drawn to scale.

Explanation:

Step1: Supplementary angle definition

Supplementary angles sum to $180^\circ$.

Step2: First system calculation

$180^\circ - 45^\circ = 135^\circ$. Adjacent angle P is supplementary.

Step3: Second system calculation

$180^\circ - 75^\circ = 105^\circ$. Adjacent angle K is supplementary.

Answer:

First system: angle P, 135
Second system: angle K, 105