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If the measure of angle one is 114 degrees and the measure of angle two equals two 𝑥 plus 21 degrees, find the value of 𝑥.
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Looking at angle one and angle two in this image, we notice that they are the two angles opposite each other when two lines cross, which makes them vertical angles.
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And vertical angles are congruent to one another.
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Since angle one and angle two are vertical angles, the measure of angle one is equal to the measure of angle two.
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114 degrees is equal to two 𝑥 plus 21 degrees.
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To solve for 𝑥, we’ll let 114 be equal to two 𝑥 plus 21.
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And now we have a two-step equation we need to solve.
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We can do that by subtracting 21 from both sides of the equation.
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114 minus 21 is 93.
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That means 93 equals two 𝑥.
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And to solve for 𝑥, we divide both sides of the equation by two.
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93 divided by two is 46.5.
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And that means 𝑥 is equal to 46.5.