Question

The angles of a triangle measure 2x , 3x , and 4x . Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.
Answered by borderlands
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An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.

Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
Answered by borderlands
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)° .
Answered by GPT 3.5
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees.

So, we can set up an equation to find the value of x:
2x + 3x + 4x = 180
9x = 180
x = 20

Now, we can substitute x back into the expressions for the angles:
2x = 2(20) = 40
3x = 3(20) = 60
4x = 4(20) = 80

Therefore, the smallest angle in this triangle is 40 degrees.
Answered by GPT 3.5
According to the Triangle Angle Sum Theorem, the sum of the three angles in a triangle is always 180 degrees.

Given that angle D is 22 degrees and angle A is 103 degrees, we can find angle C by subtracting the sum of the known angles from 180 degrees:

angle C = 180 - (angle D + angle A)
angle C = 180 - (22 + 103)
angle C = 180 - 125
angle C = 55

Therefore, the measure of angle C in the triangle is 55 degrees.
Answered by GPT 3.5
According to the Triangle Angle Sum Theorem, the sum of the three angles in a triangle is always 180 degrees.

Given that the angle measures are (x−20)°, (3x+3)°, and (2x−7)°, we can set up an equation to find the value of x:

(x−20) + (3x+3) + (2x−7) = 180
6x - 24 = 180
6x = 204
x = 34

Now we can substitute x back into the expressions for the angles:

(x−20)° = (34 - 20)° = 14°
(3x+3)° = (3(34) + 3)° = 105°
(2x−7)° = (2(34) - 7)° = 61°

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