7th Grade Math Angle Relationships Unit Test

<p>Solve for the measure of `∠IOJ`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 10, "padding": 1,"arc_label_space":0.5 }, "hide_points": false, "origin": { "x": 3, "y": 1, "label": "O","label_position": "bottom", "hide_point": false }, "lines": [ { "id": 1, "length": 7, "angle": 20, "end_vertex_label": "K", "color": "black", "extend": false }, { "id": 2, "length": 7, "angle": 78, "end_vertex_label": "J", "extend": false }, { "id": 3, "length": 7, "angle": 110, "end_vertex_label": "I", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "l", "color": "black", "hash_marks": 0, "label": "58°", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": false }, { "from_id": 1, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph >

<p>In the given figure, solve for the value of `d`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 11, "columns": 12, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 6, "label": "E","label_position": "bottom-right", "hide_point": false }, "lines": [ { "id": 1, "length": 6, "angle": 0, "end_vertex_label": "C", "color": "black", "extend": false }, { "id": 2, "length": 6, "angle": 138, "end_vertex_label": "B", "extend": false }, { "id": 3, "length": 6, "angle": 221, "end_vertex_label": "A", "extend": false }, { "id": 4, "length": 6, "angle": -85, "end_vertex_label": "D", "color": "black", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "d°", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "83°", "show_arc": false }, { "from_id": 3, "to_id": 4, "radius": "l", "color": "black", "hash_marks": 0, "label": "54°", "show_arc": false }, { "from_id": 4, "to_id": 1, "radius": "1", "color": "black", "hash_marks": 0, "label": " 85°", "show_arc": false } ], "debug": false}'></AngleGraph >

<p>In the given figure, solve for the value of `x`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 12, "columns": 12, "padding": 1 }, "hide_points": false, "origin": { "x": 6, "y": 5, "label": "E","label_position": "bottom", "hide_point": false }, "lines": [ { "id": 1, "length": 6, "angle": 30, "end_vertex_label": "C", "color": "black", "extend": false }, { "id": 2, "length": 6, "angle": 105, "end_vertex_label": "B", "extend": false }, { "id": 3, "length": 5.5, "angle": 175, "end_vertex_label": "A", "extend": false }, { "id": 4, "length": 6, "angle": -45, "end_vertex_label": "D", "color": "black", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": 1, "label": "75°", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "xs", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "m", "color": "black", "hash_marks": 0, "label": "2x°", "show_arc": true }, { "from_id": 4, "to_id": 1, "radius": "s", "color": "black", "hash_marks": 1, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph >

<p>In the diagram below, `oversetleftrightarrow(YZ)` is a straight line.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 15, "padding": 1,"arc_label_space":0.3 }, "hide_points": false, "origin": { "x": 7, "y": 2, "label": "O","label_position": "bottom", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": 0, "end_vertex_label": "Z", "color": "black", "extend": false }, { "id": 2, "length": 8, "angle": 50, "end_vertex_label": "X", "extend": false }, { "id": 3, "length": 7, "angle": 180, "end_vertex_label": "Y", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "l", "color": "black", "hash_marks": 0, "label": "130°", "show_arc": true } ], "debug": false}'></AngleGraph ><p>Solve for the measure of `∠XOZ`.</p>

<p>In the diagram below, `oversetleftrightarrow(EF)` is a straight line.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 12, "columns": 12, "padding": 1,"arc_label_space":0.3 }, "hide_points": false, "origin": { "x": 6, "y": 5, "label": "O","label_position": "bottom-left", "hide_point": true }, "lines": [ { "id": 1, "length": 7, "angle": 38, "end_vertex_label": "D", "color": "black", "extend": false }, { "id": 2, "length": 7, "angle": 142, "end_vertex_label": "E", "extend": false }, { "id": 3, "length": 7, "angle": -38, "end_vertex_label": "F", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "l", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": true }, { "from_id": 3, "to_id": 1, "radius": "s", "color": "black", "hash_marks": 0, "label": "76°", "show_arc": true } ], "debug": false}'></AngleGraph ><p>Solve for the measure of `∠DOE`.</p>

<p>`∠MON` and `∠MOL` are supplementary angles. m`∠MON = (``-4x-5)°` and m`∠MOL = (``-x - 15)°`.</p> <p>What are the measures of `∠MON` and `∠MOL`?</p>

<p>In the diagram below, `oversetleftrightarrow(JK)` and `oversetleftrightarrow(LM)` are straight lines.</p> <AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 13, "columns": 14, "padding": 1,"arc_label_space":0.3 }, "hide_points": false, "origin": { "x": 6.5, "y": 6.5, "label": "O", "hide_point": false,"label_position":"bottom-right" }, "lines": [ { "id": 1, "length": 7, "angle": -160, "end_vertex_label": "L", "color": "black" }, { "id": 2, "length": 7, "angle": -60, "end_vertex_label": "K" }, { "id": 3, "length": 7, "angle": 20, "end_vertex_label": "M" }, { "id": 4, "length": 7, "angle": 120, "end_vertex_label": "J" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash_marks": 0, "label": "(3x + 40)°", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash_marks": 0, "label": "(2x + 60)°", "show_arc": true } ], "debug": false }'></AngleGraph > <p>What are the measures of `∠JOM` and `∠LOK`?</p>

<p>Identify the relationship between each pair of angles. </p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 14, "padding": 1 }, "hide_points": false, "origin": { "x": 7, "y": 4, "label": "B", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": -25, "end_vertex_label": "C ", "color": "black " }, { "id": 2, "length": 7, "angle": 25, "end_vertex_label": " E" }, { "id": 3, "length": 7, "angle": 155, "end_vertex_label": " A" }, { "id": 4, "length": 7, "angle": 205, "end_vertex_label": " D" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash": 0, "label": " ", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relationship between `∠ABD` and `∠CBE`?</hr><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 9, "columns": 7, "padding": 1 }, "hide_points": false, "origin": { "x": 0.5, "y": 1, "label": "F", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": 50, "end_vertex_label": "H", "color": "black " }, { "id": 2, "length": 7, "angle": 87, "end_vertex_label": "G" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash": 0, "label": "37°", "show_arc": true } ], "debug": false}'></AngleGraph > <AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 9, "padding": 1 }, "hide_points": false, "origin": { "x": 7, "y": 5, "label": "J", "hide_point": false }, "lines": [ { "id": 1, "length": 7, "angle": 170, "end_vertex_label": "I", "color": "black " }, { "id": 2, "length": 7, "angle": 223, "end_vertex_label": "K" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash": 0, "label": "53°", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relation between `∠GFH` and `∠IJK`? </hr><hr><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 12, "columns": 14, "padding": 1 }, "hide_points": false, "origin": { "x": 6, "y": 6, "label": "L", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": 10, "end_vertex_label": "M", "color": "black " }, { "id": 2, "length": 7, "angle": 135, "end_vertex_label": "N" }, { "id": 3, "length": 7, "angle": 220, "end_vertex_label": "K" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "s", "color": "black", "hash": 0, "label": " ", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "m", "color": "black", "hash": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph >What is the relation between `∠NLM` and `∠NLK`? </hr></selectivedisplay>

<p>Three straight lines `oversetleftrightarrow(JM)`, `oversetleftrightarrow(LO)` and `oversetleftrightarrow(KN)` intersect at `P`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 13, "columns": 9, "padding": 1 }, "hide_points": false, "origin": { "x": 3, "y": 7, "label": "", "hide_point": false }, "lines": [ { "id": 1, "length": 8, "angle": 45, "end_vertex_label": "L", "color": "black" }, { "id": 2, "length": 4, "angle": 90, "end_vertex_label": "K" }, { "id": 3, "length": 4, "angle": 135, "end_vertex_label": "J" }, { "id": 4, "length": 3, "angle": 225, "end_vertex_label": "O", "color": "black" }, { "id": 5, "length": 6, "angle": 270, "end_vertex_label": "N", "color": "black" }, { "id": 6, "length": 6, "angle": 315, "end_vertex_label": "M", "color": "black" } ], "arcs": [ { "from_id": 4, "to_id": 6, "radius": "s", "color": "black", "hash_marks": 0, "label": " P", "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>`∠JPK` and `∠KPL`</li><li>`∠KPO` and `∠KPL`</li><li>`∠NPM` and `∠JPK`</li></ul></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": 6, "columns": 6, "padding": 1 }, "hide_points": false, "origin": { "x": 0.5, "y": 1, "label": "B", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 0, "end_vertex_label": "D", "color": "black" }, { "id": 2, "length": 5, "angle": 60, "end_vertex_label": "C" }, { "id": 3, "length": 5, "angle": 90, "end_vertex_label": "A" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "60° ", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "30° ", "show_arc": false }, { "from_id": 1, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph ></p><p>What is the relationship between `∠ABC` and `∠CBD`? </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": 8, "padding": 1 }, "hide_points": false, "origin": { "x": 4, "y": 4, "label": "T", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 40, "end_vertex_label": "R", "color": "black" }, { "id": 2, "length": 5, "angle": 135, "end_vertex_label": "P" }, { "id": 3, "length": 5, "angle": 220, "end_vertex_label": "Q" }, { "id": 4, "length": 5, "angle": 315, "end_vertex_label": "S" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "m", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph ></p><p>What is the relationship between `∠PTR` and `∠QTS`? </p></selectivedisplay><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 8, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 3, "label": "E", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": -30, "end_vertex_label": "G", "color": "black" }, { "id": 2, "length": 5, "angle": 120, "end_vertex_label": "F" }, { "id": 3, "length": 5, "angle": 150, "end_vertex_label": "D" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "150° ", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "30° ", "show_arc": true } ], "debug": false}'></AngleGraph ></p><p>What is the relationship between `∠DEF` and `∠FEG`? </p></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": 8, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 3, "label": "B", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": -30, "end_vertex_label": "D", "color": "black" }, { "id": 2, "length": 5, "angle": 136, "end_vertex_label": "C" }, { "id": 3, "length": 5, "angle": 150, "end_vertex_label": "A" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": " 166°", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "14°", "show_arc": true } ], "label_bottom": "", "debug": false}'></AngleGraph ></p> <p>What is the relationship between `∠ABC` and `∠CBD`? </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": 7, "padding": 1 }, "hide_points": true, "origin": { "x": 1, "y": 1, "label": "Q", "hide_point": true }, "lines": [ { "id": 1, "length": 5, "angle": 0, "end_vertex_label": "R", "color": "black" }, { "id": 2, "length": 5, "angle": 68, "end_vertex_label": "S" }, { "id": 3, "length": 5, "angle": 90, "end_vertex_label": "P" } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "68°", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "22°", "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 `∠PQS` and `∠SQR`?</p> </selectivedisplay><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 10, "padding": 1 }, "hide_points": false, "origin": { "x": 5, "y": 4, "label": "C", "hide_point": false }, "lines": [ { "id": 1, "length": 5, "angle": 40, "end_vertex_label": "D", "color": "black" }, { "id": 2, "length": 5, "angle": 135, "end_vertex_label": "A" }, { "id": 3, "length": 5, "angle": 220, "end_vertex_label": "B" }, { "id": 4, "length": 5, "angle": 315, "end_vertex_label": "E" } ], "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 } ]}'> </AngleGraph ></p><p>What is the relationship between `∠ACB` and `∠DCE`? </p></selectivedisplay>