Find the value of x.
An isosceles triangle is shown and the horizontal base at the bottom of the triangle extends out to the left of the triangle. The angle at the bottom right corner of the triangle and the exterior angle formed by the left side of the triangle and the horizontal line that extends at the bottom left of the image are labeled.An 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.
(1 point)
The sum of the angles in an isosceles triangle is 180 degrees.
In this triangle, we have the angle at the bottom right corner labeled as 3x + 8 degrees and the exterior angle formed at the bottom left corner labeled as 5x + 12 degrees.
Since the exterior angle is formed by extending the left side of the triangle, it is equal to the sum of the two other interior angles of the triangle.
So, we have the equation:
5x + 12 = 3x + 8 + 3x
Combining like terms:
5x + 12 = 6x + 8
Subtracting 6x and 8 from both sides:
5x - 6x = 8 - 12
-x = -4
Multiplying both sides by -1 to solve for x:
x = 4
Therefore, the value of x is 4.