Identify Angle Relationships Practice Problems

<p>Identify the relationship between each pair of angles given in the figure below. </p> <selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 4, "y": 1, "label": "D", "hide_point": true }, "lines": [ { "id": 1, "length": 7, "angle": 35, "end_vertex_label": "A", "color": "black" }, { "id": 2, "length": 6, "angle": 55, "end_vertex_label": "B" }, { "id": 3, "length": 5, "angle": 130, "end_vertex_label": "C" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relation between `∠CDB` and `∠BDA`? </hr><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 6, "padding": 1 }, "hide_points": false, "origin": { "x": 3, "y": 5, "label": "O", "label_position": "left", "hide_point": true }, "lines": [ { "id": 1, "length": 4, "angle": 55, "end_vertex_label": "E", "color": "black" }, { "id": 2, "length": 4, "angle": 120, "end_vertex_label": "J" }, { "id": 3, "length": 5, "angle": 235, "end_vertex_label": "D" }, { "id": 4, "length": 5, "angle": 300, "end_vertex_label": "K", "color": "black" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": "", "label": "", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash_marks": "", "label": "", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relation between `∠JOE` and `∠DOK`? </hr><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 1, "y": 1, "label": "Y", "hide_point": true }, "lines": [ { "id": 1, "length": 5, "angle": 20, "end_vertex_label": "Z", "color": "black" }, { "id": 2, "length": 5, "angle": 85, "end_vertex_label": "X" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": "", "label": 65, "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash_marks": "", "label": "", "show_arc": true } ], "debug": false}'></AngleGraph ><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 8, "columns": 7, "padding": 1 }, "hide_points": false, "origin": { "x": 2, "y": 6, "label": "B", "label_position": "top-left", "hide_point": true }, "lines": [ { "id": 1, "length": 5, "angle": 10, "end_vertex_label": "C", "color": "black" }, { "id": 2, "length": 5, "angle": 260, "end_vertex_label": "A" } ], "arcs": [ { "from_id": 2, "to_id": 1, "radius": "s", "color": "black", "hash_marks": "", "label": 115, "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash_marks": "", "label": "", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relation between `∠XYZ` and `∠ABC`? </hr></selectivedisplay>

<p>Identify the relationship between each pair of angles</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><P><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 6, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 1, "label": "C", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 90, "end_vertex_label": "A", "color": "black" }, { "id": 2, "length": 5, "angle": 129, "end_vertex_label": "B" }, { "id": 3, "length": 5, "angle": 180, "end_vertex_label": "D" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": 0, "label": "39°", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "m", "color": "black", "hash_marks": 0, "label": "51°", "show_arc": false }, { "from_id": 1, "to_id": 3, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph ></p><p>What is the relationship between `∠DCB` and `∠BCA`? </p></selectivedisplay><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><P><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 3, "label": "R", "hide_point": "false" }, "lines": [ { "id": 1, "length": 5, "angle": -30, "end_vertex_label": "S", "color": "black" }, { "id": 2, "length": 5, "angle": 150, "end_vertex_label": "P" }, { "id": 3, "length": 5, "angle": 179, "end_vertex_label": "Q" } ], "arcs": [ { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "29°", "show_arc": true }, { "from_id": 3, "to_id": 1, "radius": "m", "color": "black", "hash_marks": 0, "label": "151°", "show_arc": true } ], "debug": false}'></AngleGraph ></p><p>What is the relationship between `∠PRQ` and `∠QRS`?</p></selectivedisplay> <selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><P><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 9, "columns": 9, "padding": 1 }, "hide_points": true, "origin": { "x": 3, "y": 4, "label": "U", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 40, "end_vertex_label": "Y", "color": "black" }, { "id": 2, "length": 3, "angle": 135, "end_vertex_label": "X" }, { "id": 3, "length": 3, "angle": 220, "end_vertex_label": "Z" }, { "id": 4, "length": 5, "angle": 315, "end_vertex_label": "W", "color": "black" } ], "arcs": [ { "from_id": 2, "to_id": 3, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true }, { "from_id": 4, "to_id": 1, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "label_bottom": "", "debug": false}'></AngleGraph ></P></p> What is the relationship between `∠XUZ` and `∠YUW`? </p> </selectivedisplay>

<p>Three straight lines `oversetleftrightarrow(PS)`, `oversetleftrightarrow(QT)` and `oversetleftrightarrow(UR)` intersect at `V`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 11, "columns": 12, "padding": 1 }, "hide_points": false, "origin": { "x": 4, "y": 6, "label": "V", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": 20, "end_vertex_label": "R", "color": "black" }, { "id": 2, "length": 4, "angle": 110, "end_vertex_label": "Q" }, { "id": 3, "length": 4, "angle": 140, "end_vertex_label": "P" }, { "id": 4, "length": 4, "angle": 200, "end_vertex_label": "U", "color": "black" }, { "id": 5, "length": 6, "angle": 290, "end_vertex_label": "T", "color": "black" }, { "id": 6, "length": 6, "angle": 320, "end_vertex_label": "S", "color": "black" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "xs", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph ><p>Identify the relationship between the given angle pairs.</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><ul><li>`∠PVU` and `∠PVQ`</li><li>`∠PVR` and `∠SVU`</li><li>`∠SVU` and `∠RVS`</li></ul></selectivedisplay>

<p>Three straight lines `oversetleftrightarrow(DG)`,`oversetleftrightarrow(HE)` and `oversetleftrightarrow(IF)` intersect at `J`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 11, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 3, "y": 5, "label": "J", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 70, "end_vertex_label": "E", "color": "black" }, { "id": 2, "length": 4, "angle": 130, "end_vertex_label": "D" }, { "id": 3, "length": 3, "angle": 160, "end_vertex_label": "I" }, { "id": 4, "length": 4, "angle": 250, "end_vertex_label": "H", "color": "black" }, { "id": 5, "length": 6, "angle": 310, "end_vertex_label": "G", "color": "black" }, { "id": 6, "length": 6, "angle": 340, "end_vertex_label": "F", "color": "black" } ], "arcs": [ { "from_id": 3, "to_id": 4, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph ><p>Identify the relationship between the given angle pairs.</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><ul><li>`∠DJE` and `∠EJF`</li><li>`∠HJG` and `∠GJF`</li><li>`∠DJI` and `∠FJG`</li></ul></selectivedisplay>