Find Missing Angles (Simple Figures) Problems

<p>Solve for the measure of `∠NOP`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 9, "columns": 8, "padding": 1 }, "hide_points": false, "origin": { "x": 0.5, "y": 8, "label": "O", "label_position": "top", "hide_point": true }, "lines": [ { "id": 1, "length": 8, "angle": -90, "end_vertex_label": "M", "label_position": "bottom-left", "color": "black", "extend": false }, { "id": 2, "length": 8, "angle": -60, "end_vertex_label": "N", "extend": false }, { "id": 3, "length": 7, "angle": 0, "end_vertex_label": "P", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "30°", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "l", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": false }, { "from_id": 1, "to_id": 3, "radius": "l", "color": "black", "hash_marks": 0, "label": " ", "show_arc": true } ], "debug": false}'></AngleGraph >

<p>`∠IOK` is a right angle.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 10, "columns": 10, "padding": 1 }, "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>Solve for the measure of `∠IOJ`.</p>

<p>In the figure below, `oversetleftrightarrow(PQ)` is a line. Find the value of `u`</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 7, "columns": 12, "padding": 1 }, "hide_points": false, "origin": { "x": 6, "y": 1, "label": "T","label_position": "bottom", "hide_point": false }, "lines": [ { "id": 1, "length": 6, "angle": 10, "end_vertex_label": "Q", "color": "black", "extend": false }, { "id": 2, "length": 6, "angle": 107, "end_vertex_label": "R", "extend": false }, { "id": 3, "length": 6, "angle": 136, "end_vertex_label": "S", "extend": false }, { "id": 4, "length": 6, "angle": 190, "end_vertex_label": "P", "color": "black", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "l", "color": "black", "hash_marks": 0, "label": "107°", "show_arc": true }, { "from_id": 2, "to_id": 3, "radius": "s", "color": "black", "hash_marks": 0, "label": "29°", "show_arc": true }, { "from_id": 3, "to_id": 4, "radius": "m", "color": "black", "hash_marks": 0, "label": "u°", "show_arc": true } ], "debug": false}'></AngleGraph >

<p>In the given figure, solve for the value of `p`.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 13, "columns": 13, "padding": 1 }, "hide_points": false, "origin": { "x": 6.5, "y": 6, "label": "O","label_position": "bottom-right", "hide_point": false }, "lines": [ { "id": 1, "length": 6, "angle": 0, "end_vertex_label": "A", "color": "black", "extend": false }, { "id": 2, "length": 6, "angle": 73, "end_vertex_label": "B", "extend": false }, { "id": 3, "length": 6, "angle": 181, "end_vertex_label": "C", "extend": false }, { "id": 4, "length": 6, "angle": 245, "end_vertex_label": "D", "color": "black", "extend": false } ], "arcs": [ { "from_id": 1, "to_id": 2, "radius": "m", "color": "black", "hash_marks": 0, "label": "73°", "show_arc": false }, { "from_id": 2, "to_id": 3, "radius": "l", "color": "black", "hash_marks": 0, "label": "108°", "show_arc": false }, { "from_id": 3, "to_id": 4, "radius": "s", "color": "black", "hash_marks": 0, "label": "64°", "show_arc": false }, { "from_id": 4, "to_id": 1, "radius": "m", "color": "black", "hash_marks": 0, "label": " p°", "show_arc": true } ], "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(RP)` is a straight line.</p><AngleGraph data-props='{ "options": { "cell_size": 20, "rows": 8, "columns": 14, "padding": 1 }, "hide_points": false, "origin": { "x": 7, "y": 5, "label": "O","label_position": "top", "hide_point": true }, "lines": [ { "id": 1, "length": 7, "angle": 10, "end_vertex_label": "P","extend": false }, { "id": 2, "length": 7, "angle": 190, "end_vertex_label": "R","extend": false }, { "id": 3, "length": 7, "angle": 326.4, "end_vertex_label": "Q", "color": "black","extend": false } ], "arcs": [ { "from_id": 2, "to_id": 3, "radius": "m", "color": "black", "hash_marks": 0, "label": "136°", "show_arc": true }, { "from_id": 3, "to_id": 1, "radius": "s", "color": "black", "hash_marks": 0, "label": "x°", "show_arc": true } ], "debug": false}'></AngleGraph ><p>Solve for the measure of `∠POQ`.</p>

<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 >