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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers angles">
<head>
<meta charset="UTF-8" />
<title>Alternate interior angles 2</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="SOLUTION" data-ensure="abs(SOLUTION) > 5">randRangeNonZero( -20, 20 )</var>
<var id="A">randRange( 2, 9 )</var>
<var id="B" data-ensure="A * SOLUTION + B > 30 && A * SOLUTION + B < 150">randRangeNonZero( -200, 200 )</var>
<var id="C" data-ensure="C !== A && abs( A - C ) < 6 && abs( A - C ) > 1 && A * SOLUTION + B - C * SOLUTION !== 0">randRange( 2, 9 )</var>
<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( [ [ 0, 6 ], [ 1, 7 ] ] ) )</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<div class="problems">
<div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question">Solve for <code>x</code>:</p>
<p class="solution" data-forms="integer"><var>SOLUTION</var></p>
<div class="graphie" id="parallel-lines">
var eq1 = A + "x + " + B + "^\\circ";
var eq2 = C + "x + " + D + "^\\circ";
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
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 Alternate interior angles 1 that alternate interior angles are equal. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals?playlist=Geometry" data-youtube-id="gRKZaojKeP0">Watch this video</a> to understand why.</p>
<div>
<p>Set the <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> equal to the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code>.</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>
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