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°
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°.