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The problem asks to find the value of \( x \) in a triangle where the ratio of the angles is given as \( 3:5:x \), and the smallest angle is 36 degrees.

Here’s how we can solve it:

1. Since the smallest angle is 36 degrees and its ratio is 3, we can set up the equation:
   \[
   3k = 36
   \]
   Solving for \( k \):
   \[
   k = \frac{36}{3} = 12
   \]

2. Now, use this \( k \) value to find the other angles:
   - The second angle is \( 5k \):
     \[
     5k = 5 \times 12 = 60 \, \text{degrees}
     \]
   - The third angle is \( xk \):
     \[
     xk = x \times 12
     \]
   
3. Using the Triangle Angle-Sum Theorem, the sum of the angles must be 180 degrees:
   \[
   36 + 60 + 12x = 180
   \]
   Simplify:
   \[
   96 + 12x = 180
   \]
   \[
   12x = 84
   \]
   \[
   x = \frac{84}{12} = 7
   \]

So, \( x = 7 \). The three angles are 36 degrees, 60 degrees, and 84 degrees.

Would you like more details or explanations?

Here are some related questions for further practice:
1. What happens if the ratio is \( 2:3:4 \)?
2. Can you calculate the angles if the smallest angle is 45 degrees with a ratio of \( 1:2:x \)?
3. How do you verify if a triangle's angles are correct based on their ratio?
4. What other properties of a triangle can be derived from the angle measures?
5. How does the Triangle Angle-Sum Theorem apply in non-Euclidean geometry?

**Tip:** Always check if the sum of the angles equals 180 degrees in any triangle problem.

If the ratio is 3:5:x, and the smallest angle measures 36 degrees, what is x?

Learn how to find the unknown angle ratio x when given a 3:5:x ratio and the smallest angle measuring 36 degrees. This problem covers ratio calculations, using proportions, and applying the Triangle Angle-Sum Theorem. Suitable for students in Grades 6-8.

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