A triangle has the angle measures 96°, 2x°, and (x+12)°. Find the measure of the smallest angle of the triangle.

Answer 1

To find the measure of the smallest angle, we can start by setting up an equation since the sum of the angles in a triangle is 180°.

So, let's add up the three angle measures:

96° + 2x° + (x+12)° = 180°

Simplify the equation:

96° + 2x° + x° + 12° = 180°
3x + 108 = 180

Subtract 108 from both sides:

3x = 72
x = 24

Now that we have found the value of x, we can substitute it back into the expression for the smallest angle:

2x = 2(24) = 48

Therefore, the smallest angle of the triangle is 48°.