Finding Missing Angle Measures With Parallel Lines Using Angle Pairs Problems

<p>If the measure of `∠ACB = 62°`, what is the measure of `∠GFH`?</p><AngleGraph data-props='{ "options": { "cell_size": 17.5, "columns": 14, "padding": 0.2, "rows": 13 }, "hide_points": false, "debug": false, "origin": { "hide_point": false, "label": "F", "x": 10, "y": 4.7, "label_position": "top" }, "lines": [ { "angle": -40, "end_vertex_label": "H", "id": 1, "length": 5 }, { "angle": 22, "end_vertex_label": "G", "id": 2, "length": 6, "parallel_arrow": true }, { "angle": 140, "end_vertex_label": "C", "id": 3, "length": 5, "hide_arrow": true, "hide_label": true }, { "angle": 202, "end_vertex_label": "E", "id": 4, "length": 6 }, { "angle": 22, "end_vertex_label": "D", "parallel_arrow": true, "id": 5, "length": 6, "origin": { "x": 6.2, "y": 7.9, "label": "C" }, "color": "black" }, { "angle": 202, "end_vertex_label": "B", "id": 6, "length": 6, "origin": { "x": 6.2, "y": 7.9, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 140, "end_vertex_label": "A", "id": 7, "length": 5, "origin": { "x": 6.2, "y": 7.9, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 320, "end_vertex_label": "F", "id": 8, "length": 0, "origin": { "x": 6.2, "y": 7.9, "label": "C", "hide_label": true }, "color": "black" } ], "arcs": [ { "from_id": 1, "to_id": 2, "color": "red", "label": "", "radius": "xs", "show_arc": true }, { "from_id": 7, "to_id": 6, "label": "62° ", "radius": "xs", "color": "blue", "show_arc": true } ]}'></AngleGraph>

<p>If the measure of `∠ACD = 134°`, what is the measure of `∠CFG`?</p><AngleGraph data-props='{ "options": { "cell_size": 17.5, "columns": 14, "padding": 0, "rows": 9.5 }, "hide_points": false, "debug": false, "origin": { "hide_point": false, "label": "F", "x": 10.5, "y": 2.5 }, "lines": [ { "angle": -30, "end_vertex_label": "H", "id": 1, "length": 5 }, { "angle": 16, "end_vertex_label": "G", "id": 2, "length": 5, "parallel_arrow": true }, { "angle": 150, "end_vertex_label": "C", "id": 3, "length": 5.7, "hide_arrow": true, "hide_label": true }, { "angle": 196, "end_vertex_label": "E", "id": 4, "length": 5 }, { "angle": 16, "end_vertex_label": "D", "id": 5, "parallel_arrow": true, "length": 5, "origin": { "x": 5.5, "y": 5.4, "label": "C" }, "color": "black" }, { "angle": 150, "end_vertex_label": "A", "id": 6, "length": 5, "origin": { "x": 5.5, "y": 5.4, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 196, "end_vertex_label": "B", "id": 7, "length": 4.8, "origin": { "x": 5.5, "y": 5.4, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 330, "end_vertex_label": "F", "id": 8, "length": 0, "origin": { "x": 5.5, "y": 5.4, "label": "C", "hide_label": true }, "color": "black" } ], "arcs": [ { "from_id": 2, "to_id": 3, "color": "red", "label": " ", "radius": "xs", "show_arc": true }, { "from_id": 5, "to_id": 3, "label": "134°", "radius": "xs", "color": "blue", "show_arc": true } ]}'></AngleGraph>

<p>If the measure of `∠TUW = 120°`, what is the measure of `∠QRU`?</p><AngleGraph data-props='{ "options": { "cell_size": 17.5, "columns": 14, "padding": 0, "rows": 11 }, "hide_points": false, "debug": false, "origin": { "hide_point": false, "label": "U", "x": 8.5, "y": 3.7, "label_position": "top" }, "lines": [ { "angle": -50, "end_vertex_label": "W", "id": 1, "length": 5 }, { "angle": 10, "end_vertex_label": "V", "id": 2, "length": 6, "parallel_arrow": true }, { "angle": 130, "end_vertex_label": "R", "id": 3, "length": 4, "hide_arrow": true, "hide_label": true }, { "angle": 190, "end_vertex_label": "T", "id": 4, "length": 6 }, { "angle": 10, "end_vertex_label": "S", "parallel_arrow": true, "id": 5, "length": 6, "origin": { "x": 5.9, "y": 6.9, "label": "R", "label_position": "top" }, "color": "black" }, { "angle": 190, "end_vertex_label": "Q", "id": 6, "length": 5, "origin": { "x": 5.9, "y": 6.9, "label": "R", "hide_label": true }, "color": "black" }, { "angle": 130, "end_vertex_label": "P", "id": 7, "length": 3.5, "origin": { "x": 5.9, "y": 6.9, "label": "R", "hide_label": true }, "color": "black" }, { "angle": 310, "end_vertex_label": "U", "id": 8, "length": 0, "origin": { "x": 5.9, "y": 6.9, "label": "R", "hide_label": true }, "color": "black" } ], "arcs": [ { "from_id": 4, "to_id": 1, "color": "blue", "label": "120°", "radius": "xs", "show_arc": true }, { "from_id": 6, "to_id": 1, "color": "red", "label": "", "radius": "xs", "show_arc": true } ]}'></AngleGraph>

<p>If the measure of `∠DCF = 49°`, what is the measure of `∠CFE`?</p><AngleGraph data-props='{ "options": { "cell_size": 17.5, "columns": 14, "padding": 0.2, "rows": 13,"arc_label_space" : "1.5" }, "hide_points": false, "debug": false, "origin": { "hide_point": false, "label": "F", "x": 10, "y": 4.7, "label_position": "top" }, "lines": [ { "angle": -35, "end_vertex_label": "H", "id": 1, "length": 5 }, { "angle": 14, "end_vertex_label": "G", "id": 2, "length": 6, "parallel_arrow": true }, { "angle": 145, "end_vertex_label": "C", "id": 3, "length": 5, "hide_arrow": true, "hide_label": true }, { "angle": 194, "end_vertex_label": "E", "id": 4, "length": 6 }, { "angle": 14, "end_vertex_label": "D", "parallel_arrow": true, "id": 5, "length": 6, "origin": { "x": 5.7, "y": 7.7, "label": "C" }, "color": "black" }, { "angle": 194, "end_vertex_label": "B", "id": 6, "length": 5.9, "origin": { "x": 5.7, "y": 7.7, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 145, "end_vertex_label": "A", "id": 7, "length": 5, "origin": { "x": 5.7, "y": 7.7, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 325, "end_vertex_label": "F", "id": 8, "length": 0, "origin": { "x": 5.7, "y": 7.7, "label": "C", "hide_label": true }, "color": "black" } ], "arcs": [ { "from_id": 3, "to_id": 4, "color": "red", "label": "", "radius": "xs", "show_arc": true }, { "from_id": 8, "to_id": 5, "label": "49°", "radius": "xs", "color": "blue", "show_arc": true } ]}'></AngleGraph>

<p>If the measure of `∠EFH = 128°`, what is the measure of `∠ACB`?</p><AngleGraph data-props='{ "options": { "cell_size": 17.5, "columns": 14, "padding": 0.2, "rows": 13 }, "hide_points": false, "debug": false, "origin": { "hide_point": false, "label": "F", "x": 10, "y": 4.7, "label_position": "top" }, "lines": [ { "angle": -40, "end_vertex_label": "H", "id": 1, "length": 5 }, { "angle": 12, "end_vertex_label": "G", "id": 2, "length": 5.7, "parallel_arrow": true }, { "angle": 140, "end_vertex_label": "C", "id": 3, "length": 5, "hide_arrow": true, "hide_label": true }, { "angle": 192, "end_vertex_label": "E", "id": 4, "length": 6 }, { "angle": 12, "end_vertex_label": "D", "parallel_arrow": true, "id": 5, "length": 6, "origin": { "x": 6.1, "y": 8, "label": "C", "label_position": "top" }, "color": "black" }, { "angle": 192, "end_vertex_label": "B", "id": 6, "length": 5.5, "origin": { "x": 6.1, "y": 8, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 140, "end_vertex_label": "A", "id": 7, "length": 5, "origin": { "x": 6.1, "y": 8, "label": "C", "hide_label": true }, "color": "black" }, { "angle": 320, "end_vertex_label": "F", "id": 8, "length": 0, "origin": { "x": 6.1, "y": 8, "label": "C", "hide_label": true }, "color": "black" } ], "arcs": [ { "from_id": 4, "to_id": 1, "color": "blue", "label": "128°", "radius": "xs", "show_arc": true }, { "from_id": 7, "to_id": 6, "label": "", "radius": "xs", "color": "red", "show_arc": true } ]}'></AngleGraph>