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Determine whether this statement is true or false: the angles of the equilateral triangle are acute.
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First, let’s think about an equilateral triangle.
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An equilateral triangle is a triangle where all three sides are the same length.
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And because all three sides are the same length, all three angles have the same measure.
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We could say they all measure 𝑥 degrees.
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We also know that, in every triangle, the three angles must add up to 180 degrees.
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𝑥 plus 𝑥 plus 𝑥 must equal 180 degrees.
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That’s the same thing as saying three 𝑥 must equal 180 degrees.
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To find out what that missing angle is, we need to divide 180 degrees by three.
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When we do that, we find out that 𝑥 equals 60 degrees.
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Every angle inside an equilateral triangle is equal to 60 degrees.
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We know that acute angles measure less than 90 degrees.
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All three of the angles inside this equilateral triangle are less than 90 degrees.
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And that means they’re all acute.
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The statement “the angles of the equilateral triangle are acute” is true.