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

Answer 1

To find the measure of the smallest angle in the triangle, we first need to use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.

Given that the angles of the triangle measure 2x, 3x, and 4x, we can write the equation:

2x + 3x + 4x = 180

Combining the like terms:

9x = 180

Dividing both sides by 9:

x = 20

Now that we have found the value of x, we can substitute it back into the expressions for the angles:

2x = 2(20) = 40
3x = 3(20) = 60
4x = 4(20) = 80

Therefore, the smallest angle in the triangle measures 40 degrees.