organisations/520/c97d0388-4e9e-44e4-a4ef-3113893681cc.png Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
(1 point)
Responses
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
46°, 49°, and 85°
To find the measures of each angle for the triangle shown in the diagram, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Looking at the diagram, we can see that the measures of the angles are labeled as x, 3x - 2, and 5x - 6.
Using the Triangle Angle Sum Theorem, we can set up the equation:
x + (3x - 2) + (5x - 6) = 180
Combining like terms, we have:
9x - 8 = 180
Adding 8 to both sides of the equation, we get:
9x = 188
Dividing both sides by 9, we find:
x = 20.889
Now that we have the value of x, we can substitute it back into the expressions for the angle measures to find the measures of each angle.
Angle 1: x
Angle 1 = 20.889 degrees
Angle 2: 3x - 2
Angle 2 = (3 * 20.889) - 2
Angle 2 = 62.667 - 2
Angle 2 = 60.667 degrees
Angle 3: 5x - 6
Angle 3 = (5 * 20.889) - 6
Angle 3 = 104.445 - 6
Angle 3 = 98.445 degrees
Therefore, the measures of each angle for the triangle shown in the diagram are 20.889 degrees, 60.667 degrees, and 98.445 degrees.