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How to find the measures of the angles?

+1 vote
The sum of the degree measures of three angles is 180. The degree measure of the first angle is even, the degree measure of the second is 10 times the measure of the first, and the degree measure of the third is a multiple of 5.

How does one find the degree measure of each angle without guessing?
asked Jul 28, 2014 in Math by l-johnson Evoker (540 points)  

1 Answer

+2 votes
x is even.

y is a multiple of 5.

x + 10x + y = 180.

11x + y = 180.

Since x is even, there is nothing you can multiply 11 by which will get you to a number whose last digit is 5. Therefore, y must be a multiple of 10.

x must equal 10, because there is nothing else you can multiply 11 by that is an even number, that ends with a 0 and does not exceed 180.

110 + y = 180.

y = 70.

The first angle is 10, the second angle is 100, and the third angle is 70.
answered Jul 28, 2014 by emily-gan Evoker (770 points)  
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