triangle shows 8x+5 and 5x-1
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram. (1 point) Responses 46°, 50°, and 85° 46 degrees , 50 degrees , and 85 degrees 46°, 49°, and 85° 46 degrees , 49 degrees , and 85 degrees 50°, 54°, and 93° 50 degrees , 54 degrees , and 93 degrees 42°, 44°, and 79°
To find the measures of each angle for the triangle, we can use the Triangle Angle Sum Theorem. This theorem states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's set up an equation with the given angles:
(8x + 5) + (5x - 1) + (180 - x) = 180
Simplifying the equation:
8x + 5 + 5x - 1 + 180 - x = 180
12x + 4 = 180
Subtracting 4 from both sides:
12x = 176
Dividing both sides by 12:
x = 14.67
Now we can substitute x back into the angle expressions to find the measures of each angle:
Angle 1: 8x + 5 = (8)(14.67) + 5 = 117.36 + 5 = 122.36 degrees.
Angle 2: 5x - 1 = (5)(14.67) - 1 = 73.35 - 1 = 72.35 degrees.
Angle 3: 180 - x = 180 - 14.67 = 165.33 degrees.
Therefore, the measures of each angle for the triangle are approximately 122.36 degrees, 72.35 degrees, and 165.33 degrees. None of the provided answer choices match these values.