Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.

The diagram shows a triangle. The first angle of the triangle can be found by solving the equation (8x + 5). The second angle can be found by solving the equation (5x - 1), and the third angle can be found by solving (4x + 6)
Which of the answers below is correct?
46°, 50°, and 85°
42°, 44°, and 79°
50°, 54°, and 93°
46°, 49°, and 85°

1 answer

To find the measures of each angle for the triangle, we can apply the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.

Let's set up the equation to solve for the value of x:

(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, plug in the value of x into each equation to find the measures of each angle:

First angle: 8(10) + 5 = 85 degrees
Second angle: 5(10) - 1 = 49 degrees
Third angle: 4(10) + 6 = 46 degrees

Therefore, the correct answer is 46°, 49°, and 85°.