2x, 96, x + 12 Find the measure of the smallest angle of the triangle.
To find the measure of the smallest angle of the triangle, we must know that the sum of all the angles in a triangle is always 180 degrees.
Given the three angles:
2x, 96, x + 12
We can set up an equation to find the value of x:
2x + 96 + x + 12 = 180
3x + 108 = 180
3x = 72
x = 24
Now, we can substitute the value of x back into the angles to find their measures:
Angle 1: 2x = 2(24) = 48 degrees
Angle 2: 96 degrees
Angle 3: x + 12 = 24 + 12 = 36 degrees
To find the smallest angle, we compare the three angles:
48 degrees < 96 degrees < 36 degrees
Therefore, the smallest angle of the triangle measures 36 degrees.