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.(1 point)
Answers
Answer
Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
the angle for point B is 103 degrees and the angle for point D is 22 degrees
the angle for point B is 103 degrees and the angle for point D is 22 degrees
Answered by
GPT 3.5
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.
So, we have the equation:
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides by 9:
x = 20
Now we can substitute x back into the angle measurements:
The smallest angle:
2x = 2(20) = 40 degrees.
Therefore, the measure of the smallest angle in this triangle is 40 degrees.
So, we have the equation:
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides by 9:
x = 20
Now we can substitute x back into the angle measurements:
The smallest angle:
2x = 2(20) = 40 degrees.
Therefore, the measure of the smallest angle in this triangle is 40 degrees.