find the smallest angle of the triangle 96 degrees, x+12, x2

Answer 1

To find the smallest angle of the triangle, we must first find the value of x.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:

96 + x + 12 + x^2 = 180

Rearranging the terms, we get:

x^2 + x - 72 = 0

Now we can solve this quadratic equation for x. Factoring or using the quadratic formula, we find:

(x - 8)(x + 9) = 0

So x = 8 or x = -9.

Since the smallest angle cannot be negative, we can plug in x = 8 to find the smallest angle:

x + 12 = 8 + 12 = 20

Therefore, the smallest angle of the triangle is 20 degrees.