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Find the value of 𝑥.
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Well 𝑥 is the number of degrees in the measure of this angle here.
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Now in our diagram, we’ve got two intersecting lines, 𝐴𝐶 and 𝐵𝐷.
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And when you have straight lines that cross over like that, the opposite angles, vertically opposite angles in fact, are equal.
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So the measure of those two angles is equal, and the measure of those two angles are equal.
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So vertically opposite angles are equal in measure.
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Now this means that a hundred and forty-four degrees is equal to seventy-four degrees plus 𝑥 degrees.
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And we can write out the equation: a hundred and forty-four equals seventy-four plus 𝑥.
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Now if I take away seventy-four from the left-hand side and I take away seventy-four from the right-hand side, then on the right-hand side seventy-four take away seventy-four is nothing, so that just leaves me with 𝑥, and on the left-hand side a hundred and forty-four minus seventy-four is seventy.
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So the answer is 𝑥 is equal to seventy.
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And just before we finish, here’s a question.
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Is 𝑥 equals seventy degrees a correct answer?
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Well if we look carefully at the diagram, 𝑥 is the number of degrees; there’s a degree symbol above it there.
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And that means if we said 𝑥 was equal to seventy degrees, we’ll be saying that the measure of this angle here is seventy degrees degrees, and that would be wrong.
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So technically, 𝑥 equals seventy degrees is not a correct answer.
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You’d probably get one mark or half a mark.
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But if we want to be absolutely mathematically correct, the answer has to be 𝑥 is equal to just the number seventy.