A side of the triangle below has been extended to form an exterior angle of 126°. Find the value of
x
x.
We cannot solve this problem without additional information or a diagram. Please provide one of those.
To find the value of x, we can use the property that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
For a triangle, the sum of the interior angles is 180°.
Let's call the three interior angles of the triangle A, B, and C. One of the interior angles, A, is given as 126° (the exterior angle). The other two angles are remote interior angles.
So, A + B + C = 180°
We want to find the value of angle C, or x.
Since the exterior angle A is formed by extending one side of the triangle, it is equal to the sum of the two remote interior angles, B and C.
A = B + C
Substituting the known value of A from the problem (A = 126°):
126° = B + C
Now we can substitute this equation back into the first equation to solve for B and C:
126° + B + C = 180°
Simplifying:
B + C = 180° - 126°
B + C = 54°
Since we want to find the value of C or x, we can rearrange the equation to solve for C:
C = 54° - B
Now we can substitute this value of C back into the equation A = B + C to solve for B:
126° = B + (54° - B)
Simplifying:
126° = 54° + B - B
126° = 54°
Since this equation is not possible (126° does not equal 54°), it means there is no valid solution for the value of x.