SOLUTION: The second angle of a triangle is 4 times as large as the first. The third angle is 80° more than the sum of the other two angles. Find the measure of the second angle.

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Question 332804: The second angle of a triangle is 4 times as large as the first. The third angle is 80° more than the sum of the other two angles. Find the measure of the second angle.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Ordinarily when I do word problems, I just choose a variable to represent the thing I want to know. In this problem it asks for the measure of the second angle, so my initial instinct was to let represent the measure of the second angle. However, doing that means that the expression for the first angle is a fractional expression. No big deal really, it is just that I think it is tidier if you can avoid fractions. So I'm going to let represent the measure of the first angle.

That means that represents the measure of the second angle. The sum of the first and second angle is then and the third angle is more than that or

Finally, we know that the sum of the interior angles of any triangle is , so we can say:




All that is left to be done is to solve for to find the measure of the first angle and multiply that result by 4 to get the answer to this question.

John

My calculator said it, I believe it, that settles it
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