A side of the triangle below has been extended to form an exterior angle of 122°. Find the value of x
To find the value of x, we need to use the property that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Let's denote the three non-adjacent interior angles of the triangle as A, B, and C, with angle C being the one we extended to form the exterior angle.
Since the exterior angle is formed by extending side AC, angle C is adjacent to angle A. Therefore, the sum of angles A and C is equal to the measure of the exterior angle, 122°.
So, we have the equation:
A + C = 122°
Now, we need to determine the relationship between angle B and the other angles.
Since angles A, B, and C are interior angles of a triangle, the sum of their measures is always 180°. Therefore, we can write the equation:
A + B + C = 180°
We substitute the expression for the sum of angles A and C into this equation:
(A + C) + B = 180°
122° + B = 180°
Next, we isolate the variable B by subtracting 122° from both sides:
B = 180° - 122°
B = 58°
Therefore, the value of x, which represents angle B, is 58°.