A side of the triangle below has been extended to form an exterior angle of 124°. Find the value of x.
Since the exterior angle of a triangle is equal to the sum of the two remote interior angles, we have the equation: $x + 56 + 124 = 180.$ Simplifying the left side gives $x+180=180$, so $x = \boxed{0}$.
what..?
I apologize for the error in my previous response. Let me correct it:
The sum of the interior angles of a triangle is always 180 degrees. Since an exterior angle of the triangle is equal to the sum of the two remote interior angles, we have the equation: $x + 56 + 124 = 180$.
Simplifying the equation gives $x + 180 = 180$, which implies $x = 0$.
Therefore, the value of $x$ is $\boxed{0}$.
wha...?
I apologize once again for the incorrect response. Let me provide the correct solution:
In a triangle, the sum of the measures of the three interior angles is always 180 degrees.
Let's call the angle formed by extending the side of the triangle $x$.
Since the exterior angle formed is 124 degrees, the sum of the two remote interior angles is also 124 degrees.
Therefore, we have the equation: $x + (x + 56) = 124$.
Simplifying the equation gives $2x + 56 = 124$.
Subtracting 56 from both sides gives $2x = 68$.
Dividing both sides by 2 gives $x = 34$.
Therefore, the value of $x$ is $\boxed{34}$.
To solve this problem, we need to use the concept of angles in triangles.
An exterior angle of a triangle is formed when one side of the triangle is extended. In this case, the exterior angle is 124°.
To find the value of x, which represents the interior angle of the triangle, we can use the fact that the sum of the interior angles of a triangle is always 180°.
The exterior angle and the adjacent interior angle (x) will always add up to 180°.
So, we can set up the equation:
x + 124° = 180°
To solve for x, we need to isolate it. First, we subtract 124° from both sides of the equation:
x = 180° - 124°
Calculating the right side, we get:
x = 56°
Therefore, the value of x is 56°.