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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>Alternate exterior angles 2</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<div data-ensure="A * SOLUTION + B > 0 && A * SOLUTION + B < 180">
<var id="SOLUTION">randRange(6, 20) * randRangeNonZero(-1, 1)</var>
<var id="DIFFERENCE">randRange(2, 6)</var>
<var id="A">randRangeNonZero(2, 8 - DIFFERENCE) + DIFFERENCE</var>
<var id="B">DIFFERENCE * randRange(2, 15)</var>
</div>
<var id="C">A - DIFFERENCE</var>
<var id="D">A * SOLUTION + B - C * SOLUTION</var>
<var id="ANGLE">max(30, min(150, A * SOLUTION + B))</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle(randFromArray([[2, 4], [3, 5]]))</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"><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.drawMarkers(ANGLE);
graph.pl.drawTransverse(ANGLE);
graph.pl.drawAngle(KNOWN_INDEX, eq1);
graph.pl.drawAngle(UNKNOWN_INDEX, eq2, "#FFA500");
</div>
</div>
</div>
<div class="hints">
<p>Alternate exterior angles are equal to one another. <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>The <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> and the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code> are alternate exterior angles. Therefore, we can set them 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>
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