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The measures of two angles are (8x + 30)º and (12x – 40)º. What is the value of x if these two angles are congruent?

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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.

  1. Set the expressions equal: 8x + 30 = 12x - 40
  2. Move all terms containing x to one side: 8x - 12x = -40 - 30
  3. Simplify: -4x = -70
  4. Divide by -4 to find x: x = 17.5

Therefore, the value of x that makes the two angles congruent is 17.5.

User Josh Adell
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