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.
A.right,B.equilateral,C.Scalene, D.Isosceles
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.
4x = 176
So the three triangle sides are
x = 44
x + 10 = 54, and
2x -6 = 82
The triangle is scalene.
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!
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.
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.