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<!DOCTYPE html>
<html data-require="math graphie math-format">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>Complementary and supplementary angles</title>
    <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
    <div class="problems">
        <div id="complementary-angles">
            <div class="vars">
                <var id="O, A, B, C">randFromArray([
                    ["O", "A", "B", "C"],
                    ["O", "L", "M", "N"],
                    ["P", "Q", "R", "S"]
                ])</var>
                <var id="ANGLE">randRange(1, 89)</var>

                <var id="ANGLE_BOT">"\\angle " + A + O + B</var>
                <var id="ANGLE_TOP">"\\angle " + B + O + C</var>

                <var id="ANGLE_ONE, ANGLE_TWO">shuffle([ ANGLE_BOT, ANGLE_TOP ])</var>
            </div>

            <div class="question">
                <p>If <code>\angle <var>A + O + C</var></code> is a right angle and <code>m <var>ANGLE_ONE</var> = <var>ANGLE</var>^\circ</code>, what is <code>m <var>ANGLE_TWO</var></code>?</p>

                <div class="graphie">
                    init({
                        range: [ [-2, 7], [-2, 6] ],
                        scale: 40
                    });

                    var DISP_ANGLE = Math.min( Math.max( 10, ANGLE ), 80 );
                    if ( ANGLE_ONE !== ANGLE_BOT ) {
                        DISP_ANGLE = 90 - DISP_ANGLE;
                        arc( [ 0, 0 ], 1, DISP_ANGLE, 90 );
                        DISP_ANGLE *= PI / 180;
                        label( [ 2 * cos( DISP_ANGLE + ( PI / 2 - DISP_ANGLE) / 2 ) + 0.125, 2 * sin( DISP_ANGLE + ( PI / 2 - DISP_ANGLE) / 2 ) + 0.5 ], ANGLE + "^\\circ" );
                    } else {
                        arc( [ 0, 0 ], 1, 0, DISP_ANGLE );
                        DISP_ANGLE *= PI / 180;
                        label( [ 2 * cos( DISP_ANGLE / 2 ) + 0.65 , 2 * sin( DISP_ANGLE / 2 )], ANGLE + "^\\circ" );
                    }

                    path([ [0, 5], [0, 0], [5, 0] ]);
                    path([ [0, 0], [5 * cos( DISP_ANGLE ), 5 * sin( DISP_ANGLE )] ]);

                    label( [0, 0], O, "below left" );
                    label( [5, 0], A, "right" );
                    label( [0, 5], C, "above" );
                    // somewhat ick to make it look nice
                    label( [5.4 * cos( DISP_ANGLE ), 5.4 * sin( DISP_ANGLE )], B );
                </div>
            </div>

            <div class="solution" data-type="multiple">
                <span class="sol" data-forms="integer"><var>90 - ANGLE</var></span> <code>\Large{^\circ}</code>
            </div>

            <div class="hints">
                <p>From the diagram, we see that <code><var>ANGLE_BOT</var></code> and <code><var>ANGLE_TOP</var></code> are complementary angles.</p>
                <p>Therefore, <code>m <var>ANGLE_BOT</var> + m <var>ANGLE_TOP</var> = 90^\circ</code>.</p>
                <p>Thus, <code>m <var>ANGLE_TWO</var> = 90^\circ - m <var>ANGLE_ONE</var> = 90^\circ - <var>ANGLE</var>^\circ = <var>90 - ANGLE</var>^\circ</code>.</p>
            </div>
        </div>

        <div id="supplementary-angles">
            <div class="vars">
                <var id="O, A, B, C">randFromArray([
                    ["O", "A", "B", "C"],
                    ["O", "L", "M", "N"],
                    ["P", "Q", "R", "S"]
                ])</var>
                <var id="ANGLE">randRange(1, 179)</var>

                <var id="ANGLE_BOT">"\\angle " + A + O + B</var>
                <var id="ANGLE_TOP">"\\angle " + B + O + C</var>

                <var id="ANGLE_ONE, ANGLE_TWO">shuffle([ ANGLE_BOT, ANGLE_TOP ])</var>
            </div>

            <div class="question">
                <p>If <code>m \angle <var>A + O + C</var> = 180^\circ</code> and <code>m <var>ANGLE_ONE</var> = <var>ANGLE</var>^\circ</code>, what is <code>m <var>ANGLE_TWO</var></code>?</p>

                <div class="graphie">
                    init({
                        range: [ [-7, 7], [-2, 6] ],
                        scale: 40
                    });

                    var DISP_ANGLE = Math.min( Math.max( 10, ANGLE ), 170 );
                    if ( ANGLE_ONE !== ANGLE_BOT ) {
                        DISP_ANGLE = 180 - DISP_ANGLE;
                        arc( [ 0, 0 ], 1, DISP_ANGLE, 180 );
                        DISP_ANGLE *= PI / 180;
                        label( [ 2 * cos( DISP_ANGLE + ( PI - DISP_ANGLE) / 2 ) - .5, 2 * sin( DISP_ANGLE + ( PI - DISP_ANGLE) / 2 )], ANGLE + "^\\circ" );
                    } else {
                        arc( [ 0, 0 ], 1, 0, DISP_ANGLE );
                        DISP_ANGLE *= PI / 180;
                        label( [ 2 * cos( DISP_ANGLE / 2 ) + .5 , 2 * sin( DISP_ANGLE / 2 )], ANGLE + "^\\circ" );
                    }

                    path([ [-5, 0], [5, 0] ]);
                    path([ [0, 0], [5 * cos( DISP_ANGLE ), 5 * sin( DISP_ANGLE )] ]);

                    label( [0, 0], O, "below" );
                    label( [5, 0], A, "right" );
                    label( [-5, 0], C, "left" );
                    // somewhat ick to make it look nice
                    label( [5.35 * cos( DISP_ANGLE ), 5.35 * sin( DISP_ANGLE )], B );
                </div>
            </div>

            <div class="solution" data-type="multiple">
                <span class="sol" data-forms="integer"><var>180 - ANGLE</var></span> <code>\Large{^\circ}</code>
            </div>

            <div class="hints">
                <p>From the diagram, we see that <code><var>ANGLE_BOT</var></code> and <code><var>ANGLE_TOP</var></code> are supplementary angles.</p>
                <p>Therefore, <code>m <var>ANGLE_BOT</var> + m <var>ANGLE_TOP</var> = 180^\circ</code>.</p>
                <p>Thus, <code>m <var>ANGLE_TWO</var> = 180^\circ - m <var>ANGLE_ONE</var> = 180^\circ - <var>ANGLE</var>^\circ = <var>180 - ANGLE</var>^\circ</code>.</p>
            </div>
        </div>
    </div>
</div>
</body>
</html>
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