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)
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To solve for x, we can set up an equation using the property that the exterior angle of a triangle is equal to the sum of the opposite interior angles. In this case, the exterior angle at the bottom left of the triangle is equal to the sum of the bottom right angle (3x + 8) and the other interior angle (which is also 3x + 8 because it is an isosceles triangle).
So we have:
5x + 12 = (3x + 8) + (3x + 8)
Simplifying the equation, we get:
5x + 12 = 6x + 16
Moving all the terms with x to one side, we get:
5x - 6x = 16 - 12
-x = 4
Dividing both sides by -1, we get:
x = -4
Therefore, the value of x is -4.
To find the value of x, we can set up an equation using the angles in the isosceles triangle.
In an isosceles triangle, the base angles (angles opposite the equal sides) are congruent. So, we can set up the equation:
3x + 8 = 5x + 12
Now, let's solve for x:
3x - 5x = 12 - 8
-2x = 4
x = -2
Therefore, the value of x is -2.
To find the value of x in this isosceles triangle, we can use the relationships between the angles of an isosceles triangle.
First, let's consider the angle at the bottom right corner of the triangle, which is labeled as 3x + 8 degrees. This angle is equal to the other angle at the bottom left corner of the triangle, which is an exterior angle formed by the left side of the triangle and the horizontal base that extends out past the triangle, labeled as 5x + 12 degrees.
Therefore, we can set up an equation: 3x + 8 = 5x + 12.
To solve this equation, we can start by isolating the x term on one side: subtract 3x from both sides of the equation.
8 = 2x + 12.
Next, subtract 12 from both sides of the equation.
-4 = 2x.
Finally, divide both sides of the equation by 2.
-2 = x.
So, the value of x is -2.