Finding Missing Angle Measures Using Parallel Lines And Triangles Problems

<p>Use the diagram to find the value of `x`.</p><AngleGraph data-props='{ "options": { "cell_size": 25, "columns": 13, "rows": 12, "padding": 0, "arc_label_space": 0.3 }, "debug": false, "origin": { "label": "A", "label_position": "left", "x": 1, "y": 11 }, "lines": [ { "angle": 300, "end_vertex_label": "C", "id": 1, "length": 4, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "angle": 343, "end_vertex_label": "D", "id": 2, "length": 5.3, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "id": 3, "angle": 212, "color": "black", "length": 3.2, "parallel_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.5, "hide_point": true }, "end_vertex_label": "B" }, { "id": 4, "angle": 32, "color": "black", "length": 3.7, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.5, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 5, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.5, "hide_point": true, "hide_label": true }, "end_vertex_label": "A " }, { "id": 6, "angle": 300, "color": "black", "length": 3.3, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.5, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "G " }, { "id": 7, "angle": 32, "color": "black", "length": 2.6, "origin": { "label": "D", "x": 6.1, "y": 9.4, "hide_point": false, "hide_label": true }, "end_vertex_label": "E" }, { "id": 8, "angle": 343, "color": "black", "length": 4.2, "origin": { "label": "D", "x": 6.1, "y": 9.4, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "H", "hide_arrow": true }, { "id": 9, "angle": 163, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.1, "y": 9.4, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "A" }, { "id": 10, "angle": 212, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.1, "y": 9.4, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "C " }, { "id": 11, "angle": 212, "color": "black", "length": 5, "parallel_arrow": true, "origin": { "label": "G", "x": 4.7, "y": 4.6, "hide_point": true, "hide_label": true }, "end_vertex_label": "F" }, { "id": 12, "angle": 32, "color": "black", "length": 6.9, "hide_arrow": true, "origin": { "label": "G", "x": 4.7, "y": 4.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "H", "hide_label": true }, { "id": 13, "angle": 300, "color": "black", "length": 3.7, "hide_arrow": false, "origin": { "label": "G", "x": 4.7, "y": 4.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "J" }, { "id": 14, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "G", "x": 4.7, "y": 4.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "C" }, { "id": 15, "angle": 32, "color": "black", "length": 2.6, "origin": { "label": "H", "x": 10.3, "y": 8.1, "hide_point": true, "hide_label": true }, "end_vertex_label": "I" }, { "id": 16, "angle": 212, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 10.3, "y": 8.1, "hide_point": true, "hide_label": true }, "end_vertex_label": "G" }, { "id": 17, "angle": 163, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 10.3, "y": 8.1, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 18, "angle": 343, "color": "black", "length": 2.6, "hide_arrow": false, "origin": { "label": "H", "x": 10.3, "y": 8.1, "hide_point": false, "hide_label": true }, "end_vertex_label": "K" } ], "arcs": [ { "to_id": 2, "from_id": 1, "show_arc": true, "radius": "xs", "color": "black", "label": "43°" }, { "to_id": 10, "from_id": 9, "show_arc": true, "radius": "xs", "color": "black", "label": "x°" }, { "to_id": 14, "from_id": 12, "show_arc": true, "radius": "xs", "color": "black", "label": "92°" } ]}'></AngleGraph>

<p>Use the diagram to find the value of `x`.</p><AngleGraph data-props='{ "options": { "cell_size": 25, "columns": 13, "rows": 13, "padding": 0, "arc_label_space": 0.6 }, "debug": false, "origin": { "label": "A", "label_position": "left", "x": 2, "y": 11 }, "lines": [ { "angle": 300, "end_vertex_label": "C", "id": 1, "length": 5.5, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "angle": 334, "end_vertex_label": "D", "id": 2, "length": 4.1, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "id": 3, "angle": 250, "color": "black", "length": 4.4, "parallel_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 4.6, "y": 6.5, "hide_point": true }, "end_vertex_label": "B" }, { "id": 4, "angle": 70, "color": "black", "length": 2.9, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 4.6, "y": 6.5, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 5, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 4.6, "y": 6.5, "hide_point": true, "hide_label": true }, "end_vertex_label": "A " }, { "id": 6, "angle": 300, "color": "black", "length": 4.1, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 4.6, "y": 6.5, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "G ", "hide_label": true }, { "id": 7, "angle": 70, "color": "black", "length": 2.3, "origin": { "label": "D", "x": 5.6, "y": 9.3, "hide_point": false, "hide_label": true }, "end_vertex_label": "E" }, { "id": 8, "angle": 334, "color": "black", "length": 3, "origin": { "label": "D", "x": 5.6, "y": 9.3, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "H", "hide_arrow": true, "hide_label": true }, { "id": 9, "angle": 154, "color": "black", "length": 0, "origin": { "label": "D", "x": 5.6, "y": 9.3, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "A" }, { "id": 10, "angle": 250, "color": "black", "length": 0, "origin": { "label": "D", "x": 5.6, "y": 9.3, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "C " }, { "id": 11, "angle": 250, "color": "black", "length": 3.5, "parallel_arrow": true, "origin": { "label": "G", "x": 6.7, "y": 2.9, "hide_point": true, "hide_label": false, "label_position": "left" }, "end_vertex_label": "F" }, { "id": 12, "angle": 70, "color": "black", "length": 5.4, "hide_arrow": true, "origin": { "label": "G", "x": 6.7, "y": 2.9, "hide_point": false, "hide_label": true }, "end_vertex_label": "H", "hide_label": true }, { "id": 13, "angle": 300, "color": "black", "length": 3.7, "hide_arrow": false, "origin": { "label": "G", "x": 6.7, "y": 2.9, "hide_point": false, "hide_label": true }, "end_vertex_label": "J" }, { "id": 14, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "G", "x": 6.7, "y": 3, "hide_point": false, "hide_label": true }, "end_vertex_label": "C" }, { "id": 15, "angle": 70, "color": "black", "length": 3, "origin": { "label": "H", "x": 8.5, "y": 7.9, "hide_point": true, "hide_label": false, "label_position": "right" }, "end_vertex_label": "I" }, { "id": 16, "angle": 250, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 8.5, "y": 7.9, "hide_point": true, "hide_label": true }, "end_vertex_label": "G" }, { "id": 17, "angle": 154, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 8.5, "y": 7.9, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 18, "angle": 334, "color": "black", "length": 4.5, "hide_arrow": false, "origin": { "label": "H", "x": 8.5, "y": 7.9, "hide_point": false, "hide_label": true }, "end_vertex_label": "K" } ], "arcs": [ { "to_id": 2, "from_id": 1, "show_arc": true, "radius": "xs", "color": "black", "label": "x°" }, { "to_id": 5, "from_id": 4, "show_arc": true, "radius": "xs", "color": "black", "label": "62°" }, { "to_id": 16, "from_id": 17, "show_arc": true, "radius": "xs", "color": "black", "label": "84°" } ], "label_top": ""}'></AngleGraph>

<p>Use the diagram to find the value of `x`.</p><AngleGraph data-props='{ "options": { "cell_size": 25, "columns": 13, "rows": 12, "padding": 1, "arc_label_space": 0.7 }, "debug": false, "origin": { "label": "A", "label_position": "left", "x": 1, "y": 11 }, "lines": [ { "angle": 300, "end_vertex_label": "C", "id": 1, "length": 4, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "angle": 336, "end_vertex_label": "D", "id": 2, "length": 6, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "id": 3, "angle": 198, "color": "black", "length": 3.8, "parallel_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.6, "hide_point": true }, "end_vertex_label": "B" }, { "id": 4, "angle": 18, "color": "black", "length": 3.9, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 5, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.6, "hide_point": true, "hide_label": true }, "end_vertex_label": "A " }, { "id": 6, "angle": 300, "color": "black", "length": 2.8, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3, "y": 7.6, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "G ", "hide_label": true }, { "id": 7, "angle": 18, "color": "black", "length": 4, "origin": { "label": "D", "x": 6.3, "y": 8.7, "hide_point": false, "hide_label": true }, "end_vertex_label": "E" }, { "id": 8, "angle": 336, "color": "black", "length": 4.5, "origin": { "label": "D", "x": 6.3, "y": 8.7, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "H", "hide_arrow": true }, { "id": 9, "angle": 156, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.3, "y": 8.7, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "A" }, { "id": 10, "angle": 198, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.3, "y": 8.7, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "C " }, { "id": 11, "angle": 198, "color": "black", "length": 4.5, "parallel_arrow": true, "origin": { "label": "G", "x": 4.2, "y": 5.4, "hide_point": true, "label_position": "top" }, "end_vertex_label": "F" }, { "id": 12, "angle": 18, "color": "black", "length": 6.7, "hide_arrow": true, "origin": { "label": "G", "x": 4.2, "y": 5.4, "hide_point": false, "hide_label": true }, "end_vertex_label": "H", "hide_label": true }, { "id": 13, "angle": 300, "color": "black", "length": 3.7, "hide_arrow": false, "origin": { "label": "G", "x": 4.2, "y": 5.4, "hide_point": false, "hide_label": true }, "end_vertex_label": "J" }, { "id": 14, "angle": 120, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "G", "x": 4.2, "y": 5.4, "hide_point": false, "hide_label": true }, "end_vertex_label": "C" }, { "id": 15, "angle": 18, "color": "black", "length": 2.5, "origin": { "label": "H", "x": 9.7, "y": 7.2, "hide_point": true, "hide_label": true }, "end_vertex_label": "I" }, { "id": 16, "angle": 198, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 9.7, "y": 7.2, "hide_point": true, "hide_label": true }, "end_vertex_label": "G" }, { "id": 17, "angle": 156, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 9.7, "y": 7.2, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 18, "angle": 336, "color": "black", "length": 2.1, "hide_arrow": false, "origin": { "label": "H", "x": 9.7, "y": 7.2, "hide_point": false, "hide_label": true }, "end_vertex_label": "K" } ], "arcs": [ { "to_id": 2, "from_id": 1, "show_arc": true, "radius": "xs", "color": "black", "label": "36°" }, { "to_id": 10, "from_id": 9, "show_arc": true, "radius": "xs", "color": "black", "label": "x°" }, { "to_id": 13, "from_id": 11, "show_arc": true, "radius": "xs", "color": "black", "label": "78°" } ]}'></AngleGraph>

<p>Use the diagram to find the value of `x`.</p><AngleGraph data-props='{ "options": { "cell_size": 25, "columns": 13, "rows": 13, "padding": 0, "arc_label_space": 0.6 }, "debug": false, "origin": { "label": "A", "label_position": "left", "x": 3, "y": 12 }, "lines": [ { "angle": 280, "end_vertex_label": "C", "id": 1, "length": 5.2, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "angle": 324, "end_vertex_label": "D", "id": 2, "length": 4.9, "hide_point": true, "hide_label": true, "hide_arrow": true }, { "id": 3, "angle": 220, "color": "black", "length": 4.4, "parallel_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3.9, "y": 6.8, "hide_point": true }, "end_vertex_label": "B" }, { "id": 4, "angle": 40, "color": "black", "length": 3.7, "hide_arrow": true, "origin": { "label": "C", "label_position": "left", "x": 3.9, "y": 6.8, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 5, "angle": 100, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "C", "x": 3.9, "y": 6.8, "hide_point": true, "hide_label": true }, "end_vertex_label": "A " }, { "id": 6, "angle": 280, "color": "black", "length": 3.2, "hide_arrow": true, "origin": { "label": "C", "x": 3.9, "y": 6.8, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "G " }, { "id": 7, "angle": 40, "color": "black", "length": 4, "origin": { "label": "D", "x": 6.8, "y": 9.2, "hide_point": false, "hide_label": true }, "end_vertex_label": "E" }, { "id": 8, "angle": 324, "color": "black", "length": 2.7, "origin": { "label": "D", "x": 6.8, "y": 9.2, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "H", "hide_arrow": true }, { "id": 9, "angle": 144, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.8, "y": 9.2, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "A" }, { "id": 10, "angle": 220, "color": "black", "length": 0, "origin": { "label": "D", "x": 6.8, "y": 9.2, "hide_point": true, "hide_arrow": true, "hide_label": true }, "end_vertex_label": "C " }, { "id": 11, "angle": 220, "color": "black", "length": 5, "parallel_arrow": true, "origin": { "label": "G", "x": 4.5, "y": 3.7, "hide_point": true, "hide_label": true }, "end_vertex_label": "F" }, { "id": 12, "angle": 40, "color": "black", "length": 5.8, "hide_arrow": true, "origin": { "label": "G", "x": 4.5, "y": 3.7, "hide_point": false, "hide_label": true }, "end_vertex_label": "H", "hide_label": true }, { "id": 13, "angle": 280, "color": "black", "length": 3.7, "hide_arrow": false, "origin": { "label": "G", "x": 4.5, "y": 3.7, "hide_point": false, "hide_label": true }, "end_vertex_label": "J" }, { "id": 14, "angle": 100, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "G", "x": 4.5, "y": 3.7, "hide_point": false, "hide_label": true }, "end_vertex_label": "C" }, { "id": 15, "angle": 40, "color": "black", "length": 3.5, "origin": { "label": "H", "x": 9.1, "y": 7.6, "hide_point": true, "hide_label": true }, "end_vertex_label": "I" }, { "id": 16, "angle": 220, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 9.1, "y": 7.6, "hide_point": true, "hide_label": true }, "end_vertex_label": "G" }, { "id": 17, "angle": 144, "color": "black", "length": 0, "hide_arrow": true, "origin": { "label": "H", "x": 9.1, "y": 7.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "D" }, { "id": 18, "angle": 324, "color": "black", "length": 3.1, "hide_arrow": false, "origin": { "label": "H", "x": 9.1, "y": 7.6, "hide_point": false, "hide_label": true }, "end_vertex_label": "K" } ], "arcs": [ { "to_id": 2, "from_id": 1, "show_arc": true, "radius": "xs", "color": "black", "label": "x°" }, { "to_id": 5, "from_id": 4, "show_arc": true, "radius": "xs", "color": "black", "label": "60°" }, { "to_id": 17, "from_id": 15, "show_arc": true, "radius": "xs", "color": "black", "label": "104°" } ]}'></AngleGraph>