2. The angles of a triangle measure 3x, 4x, and 5.x. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.
A. 45"
B. 40°
C. 50"
D. 75°
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180°. Therefore, we can set up the equation:
3x + 4x + 5x = 180°
Combining like terms, we get:
12x = 180°
Dividing both sides by 12, we find:
x = 15°
Therefore, the smallest angle of the triangle is:
3(15°) = 45°.
Therefore, the answer is:
A. 45°
Wrong
Apologies for the incorrect response.
Since the sum of the angles in a triangle is always 180°, we can set up the equation:
3x + 4x + 5x = 180°
Combining like terms, we get:
12x = 180°
Dividing both sides by 12, we find:
x = 15°
To find the measure of the smallest angle, we substitute x back into the equation:
3(15°) = 45°
Therefore, the measure of the smallest angle in this triangle is 45°.
The correct answer is:
A. 45°