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The problem states that \( \angle FDE \) and \( \angle FDB \) are supplementary angles. Supplementary angles add up to 180°.

We are given:
\[
m\angle FDE = (3x - 15)^\circ
\]
\[
m\angle FDB = (5x + 59)^\circ
\]

Since \( \angle FDE \) and \( \angle FDB \) are supplementary, we can write the equation:
\[
(3x - 15) + (5x + 59) = 180
\]

Let's solve for \( x \).

1. Combine like terms:
\[
3x - 15 + 5x + 59 = 180
\]
\[
8x + 44 = 180
\]

2. Subtract 44 from both sides:
\[
8x = 180 - 44
\]
\[
8x = 136
\]

3. Divide by 8:
\[
x = \frac{136}{8} = 17
\]

Thus, the value of \( x \) is \( \boxed{17} \).

Would you like further details or explanations? Here are some related questions for practice:

1. What are the measures of \( \angle FDE \) and \( \angle FDB \) when \( x = 17 \)?
2. What does it mean for two angles to be supplementary?
3. How would the equation change if the angles were complementary instead of supplementary?
4. Can two obtuse angles ever be supplementary? Why or why not?
5. What is the general form for solving supplementary angle problems?

**Tip:** When dealing with supplementary angles, always ensure the sum of the angles equals 180°. This rule helps form equations for solving for unknown variables.

If m∠FDE = (3x - 15)° and m∠FDB = (5x + 59)°, find the value of x such that ∠FDE and ∠FDB are supplementary.

Find the value of x in the supplementary angles ∠FDE and ∠FDB using algebraic equations. This problem involves solving a linear equation and applying the supplementary angle theorem. Suitable for students in Grades 8-10.

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