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)
Responses
10
10
15
15
20
To find the value of x, we can set up an equation using the fact that the sum of the angles in a triangle is 180 degrees.
The angle at the bottom right corner of the triangle is 3x + 8 degrees.
The exterior angle at the bottom left of the triangle is 5x + 12 degrees.
The sum of these two angles should be equal to 180 degrees.
Therefore, we have the equation:
(3x + 8) + (5x + 12) = 180
Combining like terms:
8x + 20 = 180
Subtracting 20 from both sides:
8x = 160
Dividing both sides by 8:
x = 20
Therefore, the value of x is 20.