Question

Use the triangle angle sum theorem to find the measures of each angle for the triangle

angles in triangle: (8x + 5), (5x + 1), (4x + 6)

A) 46, 49, and 85
B) 50, 54, and 93
C) 42, 44, and 79
D) 46, 50, and 85

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measures of each angle in a triangle, we will use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in any triangle is 180 degrees.

So, we have the following equation:

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

Combine like terms:

17x + 12 = 180

Subtract 12 from both sides:

17x = 168

Divide both sides by 17:

x = 9.882

Now we can substitute this value of x back into the expressions for each angle measure:

Angle 1: (8x + 5) = (8 * 9.882 + 5) ≈ 86.058
Angle 2: (5x + 1) = (5 * 9.882 + 1) ≈ 50.412
Angle 3: (4x + 6) = (4 * 9.882 + 6) ≈ 45.528

Rounded to the nearest whole number, the measures of each angle are approximately:

Angle 1: 86 degrees
Angle 2: 50 degrees
Angle 3: 46 degrees

Therefore, the correct option is:

D) 46, 50, and 85