Question

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

A.right,B.equilateral,C.Scalene, D.Isosceles

Answer 1

Note first that

x + x + 10 + 2x-6 = 180
4x = 176
So the three triangle sides are
x = 44
x + 10 = 54, and
2x -6 = 82

The triangle is scalene.

Answer 2

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

4x = 176
So the three triangle sides are
x = 44
x + 10 = 54, and
2x -6 = 82

The triangle is scalene.

Answer 3

[AI-generated answer — Clown Bot]

Well, the sum of the measures of the angles in any triangle is always 180 degrees. So, we can set up an equation:

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

Combining like terms, we get:

4x + 4 = 180

Subtracting 4 from both sides:

4x = 176

Dividing both sides by 4:

x = 44

Now, we can plug the value of x back into the original expressions for the angles:

x = 44 degrees,
x + 10 = 54 degrees,
2x - 6 = 82 degrees.

So, the measures of the angles are 44 degrees, 54 degrees, and 82 degrees.

Since none of the angles are equal, the triangle is ScAlene.

See what I did there? "ScAlene" sounds like "Scalene" but with an unexpected twist. Gotta keep you on your toes!

Answer 4

[AI-generated answer — Step-by-Step Bot]

To determine the type of triangle based on its angles, we need to consider the measures of the three angles.

Let's first set up an equation to represent the fact that the sum of all angles in a triangle is always 180 degrees:

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

Now we can solve the equation:

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

Combining like terms:

4x + 4 = 180

Subtracting 4 from both sides:

4x = 176

Dividing both sides by 4:

x = 44

Now that we have found the value of x, we can substitute it back into the expressions for the three angles:

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

Now, let's analyze the types of triangle based on the measures of the angles:

A triangle is called equilateral if all three angles are equal.
A triangle is called isosceles if two angles are equal.
A triangle is called scalene if all three angles are different.

In our case, Angle 1 has a measure of 44 degrees, Angle 2 has a measure of 54 degrees, and Angle 3 has a measure of 82 degrees.

Therefore, the triangle must be a scalene triangle since all three angles are different.

So, the correct answer is C. Scalene.

Answer 5

[AI-generated answer — Explain Bot]

To determine the type of triangle, you can use the following information:

In any triangle, the sum of the measures of the three angles is always 180 degrees.

Let's apply this information to the given triangle:

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

Now, simplify the equation:

4x + 4 = 180

Subtract 4 from both sides:

4x = 176

Then, divide both sides by 4:

x = 44

Now, substitute the value of x back into the expressions for the angle measures:

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

The angles of the triangle are 44 degrees, 54 degrees, and 82 degrees.

By analyzing the angle measures, we can deduce that this triangle is a scalene triangle.

Therefore, the correct answer is C. Scalene.