Final answer:
To determine the value of x for two congruent angles (8x + 30)° and (12x - 40)°, the equations are set equal to each other and solved, resulting in x equals 17.5.
Step-by-step explanation:
The student asks to find the value of x given that two angles, (8x + 30)° and (12x – 40)°, are congruent. To solve this problem, we set the two expressions for the angles equal to each other because congruent angles have the same measure.
- Set the expressions equal: 8x + 30 = 12x - 40
- Move all terms containing x to one side: 8x - 12x = -40 - 30
- Simplify: -4x = -70
- Divide by -4 to find x: x = 17.5
Therefore, the value of x that makes the two angles congruent is 17.5.