Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

132 lines (114 sloc) 6.431 kb
<!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>
<p class="render-answer-area-here"></p>
<div class="graphie">
init({
range: [ [-2, 7], [-1, 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>
<p style="color:grey"><strong>NOTE:</strong> Angles not necessarily drawn to scale.</p>
</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>
<p class="render-answer-area-here"></p>
<div class="graphie">
init({
range: [ [-7, 7], [-1, 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>
<p style="color:grey"><strong>NOTE:</strong> Angles not necessarily drawn to scale.</p>
</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>
Jump to Line
Something went wrong with that request. Please try again.