In triangle ABC, if the measure of angle B is three times that of angle A, and angle C is 20 degrees more than angle A, how can I find the angle measures?

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To solve for the measures of angles A, B, and C in triangle ABC, we can use the information provided and some basic principles of geometry.

1. **Defining Variables:** Let’s denote the measure of angle A as x degrees. According to the problem, we know:

  • Angle B = 3 × angle A = 3x degrees
  • Angle C = angle A + 20 degrees = x + 20 degrees

2. **Using the Triangle Sum Theorem:** The sum of the angles in any triangle equals 180 degrees. Therefore, we can set up the following equation:

x + 3x + (x + 20) = 180

3. **Simplifying the Equation:** Combining like terms gives us:

5x + 20 = 180

4. **Solving for x:** Now, we can isolate x:

5x = 180 – 20

5x = 160

x = 32

5. **Finding Each Angle’s Measure:** Now that we have the value of x, we can find the measures of all three angles:

  • Angle A = x = 32 degrees
  • Angle B = 3x = 3 × 32 = 96 degrees
  • Angle C = x + 20 = 32 + 20 = 52 degrees

6. **Final Result:** Therefore, the measures of the angles in triangle ABC are:

  • Angle A = 32 degrees
  • Angle B = 96 degrees
  • Angle C = 52 degrees

In conclusion, the measures of angles A, B, and C are 32 degrees, 96 degrees, and 52 degrees respectively.

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