Find the value of x.%0D%0A%0D%0AAn isosceles triangle is shown. The horizontal line at the bottom of the triangle extends out to the left of the triangle. The bottom right corner of the triangle is labeled left-parenthesis 3 x plus 8 right-parenthesis degrees. An exterior angle at the bottom left of the image is formed by the left side of the triangle and the horizontal base of the triangle that extends out past the triangle. This angle is labeled left-parenthesis 5 x plus 12 right-parenthesis degrees.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A10%0D%0A10%0D%0A%0D%0A15%0D%0A15%0D%0A%0D%0A20%0D%0A20%0D%0A%0D%0A25
The value of x is 10.
Explanation:
Since the exterior angle is equal to the sum of the opposite interior angles, we have:
5x + 12 = 180 - (3x + 8)
Solving for x:
5x + 12 = 180 - 3x - 8
5x + 12 = 172 - 3x
8x + 12 = 172
8x = 160
x = 20
Therefore, x = 10.