Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle
8x+5= 5x-1= 4x+6=
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.
We can set up an equation to find the value of x. Adding up the three given expressions:
8x + 5 + 5x - 1 + 4x + 6 = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide both sides by 17:
x = 10
Now that we have the value of x, we can substitute it back into the expressions to find the measures of each angle.
1st angle: 8x + 5 = 8(10) + 5 = 80 + 5 = 85 degrees
2nd angle: 5x - 1 = 5(10) - 1 = 50 - 1 = 49 degrees
3rd angle: 4x + 6 = 4(10) + 6 = 40 + 6 = 46 degrees