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vertical_angles_2.html
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vertical_angles_2.html
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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers angles">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Vertical angles 2</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<div data-ensure="A * SOLUTION + B > 30 && A * SOLUTION + B < 150 && C !== A && abs( A - C ) < 6 && abs( A - C ) > 1 && A * SOLUTION + B - C * SOLUTION !== 0">
<var id="SOLUTION" data-ensure="abs(SOLUTION) > 5">randRangeNonZero( -20, 20 )</var>
<var id="A">randRange( 2, 9 )</var>
<var id="B">randRangeNonZero( -200, 200 )</var>
<var id="C">randRange( 2, 9 )</var>
</div>
<var id="D">A * SOLUTION + B - C * SOLUTION</var>
<var id="ANCHOR">(A*D-B*C) / (A-C)</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle( randFromArray( [ [ 2, 4 ], [ 3, 1 ] ] ) )</var>
</div>
<div class="problems">
<div>
<p class="question">Solve for <code>x</code>:</p>
<div class="solution" data-type="multiple">
<p><code>x=</code> <span class="sol" data-type="rational"><var>SOLUTION</var></span></p>
</div>
<div class="graphie" id="lines">
var eq1 = A + "x + " + B + "^\\circ";
var eq2 = C + "x + " + D + "^\\circ";
init({
range: [ [ -1, 5 ], [-1, 1] ]
});
graph.pl = new ParallelLines( 0, 0, 4, 0, 0 );
graph.pl.draw();
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, eq1 );
graph.pl.drawAngle( UNKNOWN_INDEX, eq2, "#FFA500" );
</div>
</div>
</div>
<div class="hints">
<p>We learned in Vertical angles 1 that vertical angles are equal. <a class="related-video" href="/video/proof-vertical-angles-are-equal" data-youtube-id="wRBMmiNHQaE">Watch this video</a> to understand why.</p>
<div>
<p>Set the angle measures equal to one another.</p>
<p><code>\color{<var>BLUE</var>}{<var>A</var>x + <var>B</var>} = \color{<var>ORANGE</var>}{<var>C</var>x + <var>D</var>}</code></p>
</div>
<div data-if="A > C" data-unwrap>
<div>
<p>Subtract <code>\color{<var>PINK</var>}{<var>C</var>x}</code> from both sides.</p>
<p><code>(<var>A</var>x + <var>B</var>) \color{<var>PINK</var>}{- <var>C</var>x} = (<var>C</var>x + <var>D</var>) \color{<var>PINK</var>}{- <var>C</var>x}</code></p>
<p><code><var>A - C</var>x + <var>B</var> = <var>D</var></code></p>
</div>
<div>
<p><var>B > 0 ? "Subtract" : "Add"</var> <code>\color{<var>PINK</var>}{<var>abs(B)</var>}</code> <var>B > 0 ? "from" : "to"</var> both sides.</p>
<p><code>(<var>A - C</var>x + <var>B</var>) \color{<var>PINK</var>}{+ <var>-B</var>} = <var>D</var> \color{<var>PINK</var>}{+ <var>-B</var>}</code></p>
<p><code><var>A - C</var>x = <var>D - B</var></code></p>
</div>
<div>
<p>Divide both sides by <code>\color{<var>PINK</var>}{<var>A - C</var>}</code>.</p>
<p><code>\dfrac{<var>A - C</var>x}{\color{<var>PINK</var>}{<var>A - C</var>}} = \dfrac{<var>D - B</var>}{\color{<var>PINK</var>}{<var>A - C</var>}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>x = <var>SOLUTION</var></code></p>
</div>
</div>
<div data-else data-unwrap>
<div>
<p>Subtract <code>\color{<var>PINK</var>}{<var>A</var>x}</code> from both sides.</p>
<p><code>(<var>A</var>x + <var>B</var>) \color{<var>PINK</var>}{- <var>A</var>x} = (<var>C</var>x + <var>D</var>) \color{<var>PINK</var>}{- <var>A</var>x}</code></p>
<p><code><var>B</var> = <var>C - A</var>x + <var>D</var></code></p>
</div>
<div>
<p><var>D > 0 ? "Subtract" : "Add"</var> <code>\color{<var>PINK</var>}{<var>abs(D)</var>}</code> <var>D > 0 ? "from" : "to"</var> both sides.</p>
<p><code><var>B</var> \color{<var>PINK</var>}{+ <var>-D</var>} = (<var>C - A</var>x + <var>D</var>) \color{<var>PINK</var>}{+ <var>-D</var>}</code></p>
<p><code><var>B - D</var> = <var>C - A</var>x</code></p>
</div>
<div>
<p>Divide both sides by <code>\color{<var>PINK</var>}{<var>C - A</var>}</code>.</p>
<p><code>\dfrac{<var>B - D</var>}{\color{<var>PINK</var>}{<var>C - A</var>}} = \dfrac{<var>C - A</var>x}{\color{<var>PINK</var>}{<var>C - A</var>}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code><var>SOLUTION</var> = x</code></p>
</div>
</div>
</div>
</div>
</body>
</html>