Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)°, (3x+3)°, and (2x−7)°.(1 point)

Answer 1

The Triangle Angle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees.

Therefore, we can set up the equation:

(x-20) + (3x+3) + (2x-7) = 180

Simplifying the equation, we get:

6x - 24 = 180

Adding 24 to both sides, we get:

6x = 204

Dividing both sides by 6, we get:

x = 34

Now we can substitute the value of x back into the angle measures:

Largest angle = 3x + 3
= 3(34) + 3
= 102 + 3
= 105 degrees

Therefore, the largest angle in the triangle is 105 degrees.

Answer 2

positive

Answer 3

Apologies for the confusion. Let's solve for the largest angle using the given angle measures.

The largest angle in the triangle is the angle measure that is the greatest among the three given angles.

Given angle measures: (x-20)°, (3x+3)°, and (2x-7)°

To find the largest angle, we can compare the expressions for each angle and determine which one is the greatest.

Expression for the first angle: x-20
Expression for the second angle: 3x+3
Expression for the third angle: 2x-7

We need to find the value of x that makes one of these expressions the greatest.

To do this, we can set up inequalities.

For the first angle:
x-20 > 0
x > 20

For the second angle:
3x+3 > 0
3x > -3
x > -1

For the third angle:
2x-7 > 0
2x > 7
x > 7/2

From the above inequalities, we can see that x > 20 satisfies all three inequalities.

Now we substitute x = 20 into each expression to find the measure of the largest angle.

First angle: (x-20) = (20-20) = 0 degrees
Second angle: (3x+3) = (3*20+3) = 63 degrees
Third angle: (2x-7) = (2*20-7) = 33 degrees

From these calculations, we can conclude that the second angle with a measure of 63 degrees is the largest angle in the triangle.