Use the Triangle Angle Sum Theorem then find the largest angle in a triangle with angle measures of (x−20)°, (3x+3)°, and (2x−7)°.
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.
So, we can set up an equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplifying the equation:
6x - 14 = 180
Adding 14 to both sides:
6x = 194
Dividing by 6:
x = 32.33
Now we can substitute x back into the angle measures to find each angle:
(x-20) = 12.33°
(3x+3) = 99.99°
(2x-7) = 57.66°
Therefore, the largest angle in the triangle is 99.99°.
To find the largest angle in a triangle, we first need to use the Triangle Angle Sum Theorem. According to this theorem, the sum of the angles in a triangle is always 180 degrees.
So, let's set up the equation using the angle measures given:
(x-20) + (3x+3) + (2x-7) = 180
Now, let's simplify and solve for x:
6x - 24 = 180
6x = 204
x = 34
Now we can find the measures of each angle using the value of x:
1. First angle: (x-20)° = (34-20)° = 14°
2. Second angle: (3x+3)° = (3*34+3)° = 105°
3. Third angle: (2x-7)° = (2*34-7)° = 61°
To determine the largest angle, we compare the measures obtained:
The largest angle in the triangle is 105°.
To find the largest angle in a triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's apply this theorem to the given triangle:
Angle 1: (x - 20)°
Angle 2: (3x + 3)°
Angle 3: (2x - 7)°
According to the Triangle Angle Sum Theorem, the sum of these three angles should be equal to 180 degrees:
(x - 20) + (3x + 3) + (2x - 7) = 180
Now, let's solve the equation:
Combining like terms:
6x - 24 = 180
Adding 24 to both sides:
6x = 204
Dividing both sides by 6:
x = 34
Now that we have found the value of x, we can substitute it back into the expressions for each angle:
Angle 1: (x - 20)° = (34 - 20)° = 14°
Angle 2: (3x + 3)° = (3 * 34 + 3)° = 105°
Angle3: (2x - 7)° = (2 * 34 - 7)° = 61°
Therefore, the largest angle in the triangle is 105°.