Question

There is a triangle with the measures (5x-1), (8x+5) and (4x+6). Find the measures for each angle.

Answer 1

To find the measures of the angles in the triangle, we need to use the fact that the sum of angles in a triangle is always 180 degrees.

Let's label the angles A, B, and C. Using the given measures of the sides, we can set up the following equation:

(5x-1) + (8x+5) + (4x+6) = 180

Simplifying the equation:

5x - 1 + 8x + 5 + 4x + 6 = 180
17x + 10 = 180
17x = 180 - 10
17x = 170
x = 170 / 17
x = 10

Now that we have found the value of x, we can substitute it back into the expressions for the side measures to find the angles:

Angle A: 5x-1 = 5(10)-1 = 50 - 1 = 49 degrees
Angle B: 8x+5 = 8(10)+5 = 80 + 5 = 85 degrees
Angle C: 4x+6 = 4(10)+6 = 40 + 6 = 46 degrees

Therefore, the measures of the angles are 49 degrees, 85 degrees, and 46 degrees.