an isosceles triangle has two angles of the same measure. if the angle represented by y measures 3 degrees less than the angle x, find the measures of all the angles of the triangle

Answer 1

The sum of the angles of a euclidean triangle is always 180 degrees. If you set up the sum, it will look like:

x+x+y= 180.

Since y is three degrees less than x, we can set y= x-3. The equation then becomes:

x+x+x-3= 180. We can then change that to 3x=183. Next we have x=183/3, so x = 61

Since y= x-3, we get y= 61-3 -> y= 58

To check your answer, add up the angles: 61 + 61 + 58 = 180

Answer 2

Assuming that angle x represents one of the two angles that have the same value, you have:

y = x - 3 ("y is three degrees less than the angle x)

and

2*x + y = 180 --> 2*x + (x - 3) = 3*x - 3 = 180 add 3 to both sides of the equation, get 3*x = 183

--> x = 61

If y is one of the two angles with the same value, then you have:

x + 2*y = 180 --> x + 2*(x - 3) = x + 2x - 6 = 3x - 6 = 180 ---> 3x = 186 --> x = 62