Use the image to answer the question. Find the measure of the smallest angle of the triangle

Question

the triangle labels 96 2x and x + 12

Answer 1

To find the measure of the smallest angle of the triangle, we need to use the fact that the sum of all angles in a triangle is equal to 180 degrees.

Let's assign the labeled angles in the triangle as follows:
Angle 1 = 96 degrees
Angle 2 = 2x degrees
Angle 3 = x + 12 degrees

Since we know that the sum of all angles in a triangle is equal to 180 degrees, we can write the equation:

Angle 1 + Angle 2 + Angle 3 = 180 degrees

Plugging in the values we have:
96 + 2x + (x + 12) = 180

Combining like terms:
96 + 3x + 12 = 180

Simplifying:
3x + 108 = 180

Subtracting 108 from both sides:
3x = 72

Dividing both sides by 3:
x = 24

Since we are looking for the smallest angle, we substitute x = 24 into Angle 2:
Angle 2 = 2x = 2(24) = 48 degrees

Therefore, the measure of the smallest angle of the triangle is 48 degrees.