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The ratio among the measures of the angles of a triangle is 16 to 10 to 19.
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Find the measure of the greatest angle of this triangle.
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So we don’t know the measures of the individual angles.
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But we do know the ratio that exists between them.
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We also know key facts about the angles in triangles, which is that the angle sum of any triangle is 180 degrees.
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We’ll answer this question using the concept of the sum of the parts of a ratio.
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By adding together the three parts of the ratio, we see that the total parts is equal to 45.
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As the angle sum in the triangle is 180 degrees, this means that these 45 parts are equal to 180 degrees.
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All these parts are of equal size.
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So to find the size of one part, we can divide both sides of the ratio by 45.
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One part is equal to four degrees.
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We’re only asked to find the measure of one of the angles, the greatest angle.
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This is the angle with the most parts.
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So it’s the part of the ratio with 19 parts.
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To find the value of 19 parts, we now multiply both sides of the ratio by 19.
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The measure of the greatest angle in the triangle is 76 degrees.
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Now a sensible check here would also be to calculate the measures of the other two angles and confirm that the angle sum is indeed 180 degrees.
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To find the measure of the angle with 16 parts, we multiply one part by 16.
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16 parts is equivalent to 64 degrees.
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To find the measure of the angle with 10 parts, we multiply one part by 10.
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10 parts is equal to 40 degrees.
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By summing the measures of the three calculated angles together, we confirm that their sum is indeed 180 degrees.
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And this just helps have a little bit more confidence in our answer.
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The measure of the greatest angle in the triangle is 76 degrees.