Step-by-step explanation:
Since ABC is a triangle,
Angle A + Angle B + Angle C = 180 (Sum of angles in a triangle)
given Angle A = 3x + 1
Angle B = 4x - 17
Angle C = 5x - 20
[tex]3x + 1 + (4x - 17) + (5x - 20) = 180 \\ 3x + 4x + 5x + 1 - 17 - 20 = 180 \\ 12x - 36 = 180 \\ 12x = 180 + 36 \\ 12x = 216 \\ x = 216 \div 12 \\ = 18[/tex]
Now substitute x into all 3 angles.
A = 3(18) + 1 = 54 + 1 = 55 degrees
B = 4(18) - 17 = 72 - 17 = 55 degrees
C = 5(18) - 20 = 90 - 20 = 70 degrees
Since Angle A = Angle B but not equal to Angle C,
Triangle ABC is a isosceles triangle as 2 angles must be the same for it to be a isosceles triangle.
