Answer:
the value of y is 17
Explanation:
The sum of the three angles in a triangle is always equal to 180 degrees. So, you can set up the equation:
3y + 13 + 5y - 5 + 2y + 2 = 180
Now, combine the like terms on the left side of the equation:
(3y + 5y + 2y) + (13 - 5 + 2) = 180
10y + 10 = 180
Now, isolate 10y by subtracting 10 from both sides of the equation:
10y = 180 - 10
10y = 170
Finally, divide by 10 to solve for y:
y = 170 / 10
y = 17
So, the value of y is 17, and each angle of the triangle can be calculated by substituting this value into the expressions:
1st angle: 3y + 13 = 3 * 17 + 13 = 51 + 13 = 64 degrees
2nd angle: 5y - 5 = 5 * 17 - 5 = 85 - 5 = 80 degrees
3rd angle: 2y + 2 = 2 * 17 + 2 = 34 + 2 = 36 degrees
The angles of the triangle are 64 degrees, 80 degrees, and 36 degrees, and their sum is indeed 180 degrees, as expected for a triangle.