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Question 116501: find the measure of the third angle of a triangle in which the measures of two angles are w and (w+20).
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The sum of the angles in a triangle is 180 degrees.
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Suppose that you knew one of the angles in the triangle was 20 degrees and another angle in
the triangle was 80 degrees. How would you find the third angle? You can do it by adding the
two angles that you know ... 20 degrees + 80 degrees = 100 degrees. Since these two angles
provide 100 degrees of the 180 degrees in the triangle, the third angle must provide the
rest. Therefore, the third angle must be 180 degrees minus 100 degrees and this is 80 degrees.
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The problem you are given can be worked in a similar manner.
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You are given that two of the angles of a triangle are w and w + 20. If you add these two
angles you get:
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w + (w + 20) = w + w + 20 = 2w + 20
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The third angle of the triangle must be the remainder after you subtract the sum of the two
known angles from 180 degrees. So subtract 2w + 20 from 180 degrees:
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180 - (2w + 20)
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If you have terms inside a set of parentheses that is preceded by a minus sign, you can remove
the parentheses if you change the signs of the terms inside the parentheses. Applying that
rule we remove the parentheses by changing the 2w inside the parentheses to -2w and the +20
inside the parentheses to -20. So the problem becomes:
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180 - 2w - 20
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Combine the 180 and the -20 to get 160 and the answer becomes that the third angle equals:
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160 - 2w
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Check: do the three angles: w, w + 20, and 160 - 2w add up to be 180 degrees?
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w + w + 20 + 160 - 2w
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The w + w -2w equals 2w - 2w and this cancels out to zero. What remains is 20 + 160 and
this does equal 180. So the three angles correctly add to 180 degrees. The answer that
the third angle is 160 - 2w therefore is correct.
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Hope this helps you to understand the problem.
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