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A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.
Find the measure of the smallest angle of the triangle.(1 point)
To find the measure of the smallest angle of the triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
In this case, we are given that one angle measures 2x, another angle measures 96 degrees, and the third angle measures x + 12 degrees.
So, we can set up the following equation:
2x + 96 + x + 12 = 180
Combine like terms:
3x + 108 = 180
Subtract 108 from both sides:
3x = 72
Divide both sides by 3:
x = 24
Now that we know x = 24, we can substitute this value into the expression for the smallest angle: x + 12.
So, the measure of the smallest angle of the triangle is:
24 + 12 = 36 degrees