What is the distance from his house to school?
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We are given that BA is perpendicular to BD, so that must mean that <em>m∠ABD </em>is a right angle, or 90º. This means: (8x - 10) + (4x + 52) = 90º, since both of the angles add up to become a right angle. We have to solve for x in order to find <em>m∠CBD.</em>
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<u>PART 1</u>
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Equation: (8x - 10) + (4x + 52) = 90
Let's add the like values together first.
Let's subtract 42 from both sides of the equation to isolate the variable we are solving for, x. Our goal is to isolate it completely to get a value that is equal to x.
Divide both sides by 12 to get our final answer for x.
<u>PART 2</u>
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Now that we have x, we simply plug it into our equation for <em>m∠CBD. </em>
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Multiply 4 and add 52.