Question

If the measures, in degrees, of the three angles of a triangle are x, x+10, and 2x-6, the triangle must be

1) Isosceles
2) Equilateral
3) Right
d) Scalene

Answer 1

The triangle is scalene. Correct option is d.

Step-by-step explanation:

To determine the type of triangle based on the measures of its angles, we can set up an equation:

x + (x+10) + (2x-6) = 180

Simplifying, we have: 4x + 4 = 180

Then, we solve for x:

4x = 176

x = 44

Substituting x back into the given measures:

• Angle 1: x = 44 degrees
• Angle 2: x + 10 = 44 + 10 = 54 degrees
• Angle 3: 2x - 6 = 2(44) - 6 = 82 degrees

Since all three angles have different measures, the triangle is Scalene.