WEBVTT
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π΄π΅ is a straight line.
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Find the value of π₯.
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Looking at the diagram, we can see that we have this straight line π΄π΅ and then three angles that sit together on this straight line.
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Weβre asked to find the value of π₯, which is used in expressions for two of the angles.
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The key fact that we need to use to answer this question is that angles on a straight line sum to 180 degrees.
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We have expressions for two of the angles in terms of π₯.
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Theyβre six π₯ degrees and nine π₯ degrees.
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And the third angle has been labelled using a little square, which means itβs a right angle, 90 degrees.
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We can, therefore, form an equation, using the fact that these three angles must sum to 180 degrees.
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Six π₯ degrees plus 90 degrees plus nine π₯ degrees is equal to 180 degrees.
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To find the value of π₯, we need to solve this equation the first step is to simplify the equation by grouping like terms.
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As we have six π₯ degrees plus nine π₯ degrees, this simplifies to 15π₯ degrees.
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So we have 15π₯ degrees plus 90 degrees is equal to 180 degrees.
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The next step is to subtract 90 degrees from each side of the equation.
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And it gives 15π₯ degrees is equal to 90 degrees.
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Now, we have 15π₯ degrees.
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But we just want to know what π₯ degrees is equal to.
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So we need to divide both sides of the equation by 15.
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90 divided by 15 is six.
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So we have π₯ degrees is equal to six degrees.
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So weβve solved the equation and found the value of π₯.
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Now both sides have a unit included with them, this degree symbol, which means that the value of π₯ is just the numeric or number value of the right-hand side.
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So we have that the value of π₯ is six.