Use the triangle angle sum theorem to find the measure of the angles for the triangle in the diagram
(4x+6)
(5x-1)
(8x+5)
The triangle angle sum theorem states that the sum of the measures of the angles in any triangle is always equal to 180 degrees.
Let's denote the angles of the triangle as A, B, and C. We can set up the equation:
A + B + C = 180
Now, let's substitute the given expressions for the measures of the angles:
4x + 6 + 5x - 1 + 8x + 5 = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide by 17:
x = 10
Now, substitute x = 10 back into the expressions for the angles:
Angle A = 4(10) + 6 = 40 + 6 = 46 degrees
Angle B = 5(10) - 1 = 50 - 1 = 49 degrees
Angle C = 8(10) + 5 = 80 + 5 = 85 degrees
Therefore, the measures of the angles for the triangle are:
Angle A = 46 degrees
Angle B = 49 degrees
Angle C = 85 degrees