The measures, in degrees, of the three angles are x, x+10, and 2x-6. Find the measure of all three angles of the triangle.
The interior angles of a triangle always add up to 180°
x + x + 10° + 2 x - 6° = 180°
4 x + 4° = 180° Subtract 4° to both sides
4 x + 4° - 4° = 180° - 4°
4 x = 176° Divide both sides by 4
4 x / 4 = 176° / 4
x = 44°
Angles :
x = 44°
x + 10° = 44° + 10° = 54°
2 x - 6° = 2 * 44° - 6° = 88° - 6° = 82°
To find the measures of the three angles of the triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the measures of the three angles as x, x+10, and 2x-6.
According to the given information, the sum of the angles in the triangle is 180 degrees. So, we can write the equation:
x + (x+10) + (2x-6) = 180
Simplifying the equation, we have:
4x + 4 = 180
Subtracting 4 from both sides of the equation:
4x = 176
Dividing both sides of the equation by 4:
x = 44
Now, we can substitute the value of x back into the expressions for the angles to find their measures:
First angle: x = 44 degrees
Second angle: x + 10 = 44 + 10 = 54 degrees
Third angle: 2x - 6 = 2(44) - 6 = 88 - 6 = 82 degrees
Therefore, the measures of the three angles of the triangle are 44 degrees, 54 degrees, and 82 degrees.
To find the measures of the three angles, we can set up an equation based on the given information:
The sum of the measures of the angles in a triangle is always 180 degrees.
So, we can write the equation:
x + (x + 10) + (2x - 6) = 180
Now, let's solve this equation to find the value of x:
Combine like terms:
4x + 4 = 180
Subtract 4 from both sides:
4x = 176
Divide both sides by 4:
x = 44
Now that we have the value of x, we can find the measures of all three angles:
Angle 1: x = 44 degrees
Angle 2: x + 10 = 44 + 10 = 54 degrees
Angle 3: 2x - 6 = 2(44) - 6 = 88 - 6 = 82 degrees
Therefore, the measures of the three angles of the triangle are: 44 degrees, 54 degrees, and 82 degrees.