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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>Supplementary angles</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="find-hypotenuse">
<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>, in degrees?</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-forms="integer"><var>180 - ANGLE</var></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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