Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.triangle shows 8x+5 and 5x-1 and 4x+6 (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 in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
Let's solve for the measures of each angle:
Let the measures of the angles be denoted as A, B, and C, with A representing 8x+5, B representing 5x-1, and C representing 4x+6.
According to the Triangle Angle Sum Theorem, we have the equation:
A + B + C = 180
Substituting the given expressions for A, B, and C into the equation, we have:
(8x+5) + (5x-1) + (4x+6) = 180
Combining like terms, we have:
17x + 10 = 180
Subtracting 10 from both sides of the equation, we have:
17x = 170
Dividing both sides of the equation by 17, we have:
x = 10
Now, substituting the value of x back into the expressions for A, B, and C, we have:
A = 8(10) + 5 = 85
B = 5(10) - 1 = 49
C = 4(10) + 6 = 46
Therefore, the measures of each angle in the triangle are 85 degrees, 49 degrees, and 46 degrees.