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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 data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<div data-ensure="A * SOLUTION + B > 30 && A * SOLUTION + B < 150 && abs(A - C) < 6 && 180 - (A + C) * SOLUTION - B !== 0">
<var id="SOLUTION">randRange(6, 20) * randRangeNonZero(-1, 1)</var>
<var id="A">randRange(2, 8)</var>
<var id="B">randRangeNonZero(-200, 200)</var>
<var id="C">randRangeExclude(2, 9, [A, A - 1, A + 1])</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>
<p class="render-answer-area-here"></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: [[-4, 4], [-1, 1]],
scale: 60
});
graph.pl = new ParallelLines(0, 0, 4, 0, 0);
graph.pl.draw();
graph.pl.drawTransverse(KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR);
graph.pl.drawAngle(KNOWN_INDEX, eq1);
graph.pl.drawAngle(UNKNOWN_INDEX, eq2, GREEN);
</div>
</div>
</div>
<div class="hints">
<p>We learned in Vertical angles 1 that vertical angles are equal. <a href="/video/proof-vertical-angles-are-equal" class="related-video" 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>\blue{<var>A</var>x + <var>B</var>^\circ} = \green{<var>C</var>x + <var>D</var>^\circ}</code></p>
</div>
<div data-if="A > C" data-unwrap="">
<div>
<p>Subtract <code>\pink{<var>C</var>x}</code> from both sides.</p>
<p><code>
(<var>A</var>x + <var>B</var>^\circ) \pink{- <var>C</var>x} =
(<var>C</var>x + <var>D</var>^\circ) \pink{- <var>C</var>x}
</code></p>
<p><code><var>A - C</var>x + <var>B</var>^\circ = <var>D</var>^\circ</code></p>
</div>
<div>
<p data-if="B > 0">Subtract <code>\pink{<var>abs(B)</var>}^\circ</code> from both sides.</p>
<p data-else="">Add <code>\pink{<var>abs(B)</var>}^\circ</code> to both sides.</p>
<p><code>
(<var>A - C</var>x + <var>B</var>^\circ) \pink{+ <var>-B</var>^\circ} =
<var>D</var> \pink{+ <var>-B</var>^\circ}
</code></p>
<p><code><var>A - C</var>x = <var>D - B</var>^\circ</code></p>
</div>
<div>
<p>Divide both sides by <code>\pink{<var>A - C</var>}</code>.</p>
<p><code>\dfrac{<var>A - C</var>x}{\pink{<var>A - C</var>}} = \dfrac{<var>D - B</var>^\circ}{\pink{<var>A - C</var>}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>x = <var>SOLUTION</var>^\circ</code></p>
</div>
</div>
<div data-else="" data-unwrap="">
<div>
<p>Subtract <code>\pink{<var>A</var>x}</code> from both sides.</p>
<p><code>
(<var>A</var>x + <var>B</var>^\circ) \pink{- <var>A</var>x} =
(<var>C</var>x + <var>D</var>^\circ) \pink{- <var>A</var>x}
</code></p>
<p><code><var>B</var>^\circ = <var>C - A</var>x + <var>D</var>^\circ</code></p>
</div>
<div>
<p data-if="D > 0">Subtract <code>\pink{<var>abs(D)</var>^\circ}</code> from both sides.</p>
<p data-else="">Add <code>\pink{<var>abs(D)</var>^\circ}</code> to both sides.</p>
<p><code>
<var>B</var>^\circ \pink{+ <var>-D</var>^\circ} =
(<var>C - A</var>x + <var>D</var>^\circ) \pink{+ <var>-D</var>^\circ}
</code></p>
<p><code><var>B - D</var>^\circ = <var>C - A</var>x</code></p>
</div>
<div>
<p>Divide both sides by <code>\pink{<var>C - A</var>}</code>.</p>
<p><code>\dfrac{<var>B - D</var>^\circ}{\pink{<var>C - A</var>}} = \dfrac{<var>C - A</var>x}{\pink{<var>C - A</var>}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code><var>SOLUTION</var>^\circ = x</code></p>
</div>
</div>
</div>
</div>
</body>
</html>