Final answer:
The given triangle △ABC with angle measures m∠A=7x-10, m∠B=4x+20, and m∠C=5x+10 is equilateral.
Step-by-step explanation:
The given triangle △ABC has angle measures m∠A=7x-10, m∠B=4x+20, and m∠C=5x+10. To classify the triangle, we need to determine if the triangle has any equal sides. If all sides are equal, the triangle is equilateral. If two sides are equal, the triangle is isosceles. If all sides are different, the triangle is scalene.
To determine the values of x, we can set the angle measures equal to each other and solve for x.
m∠A = m∠B → 7x-10 = 4x+20
m∠B = m∠C → 4x+20 = 5x+10
Solving these equations, we get x = 10.
Substituting the value of x back into the angle measures, we have m∠A = 7(10)-10 = 60 degrees, m∠B = 4(10)+20 = 60 degrees, and m∠C = 5(10)+10 = 60 degrees.
Since all angle measures are equal, the triangle △ABC is equilateral.