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The problem presents a circle with four points labeled \( A \), \( B \), \( C \), and \( D \). You are asked to find the value of \( x \) that satisfies the given angle relationships. 

We are given the following angles:

- \( \angle BAD = (2x - 10)^\circ \)
- \( \angle ABC = (4x - 10)^\circ \)
- \( \angle BCD = (5x - 5)^\circ \)
- \( \angle ADC = (3x + 15)^\circ \)

### Step-by-Step Solution:

In a cyclic quadrilateral, the opposite angles sum up to 180°. This means:
- \( \angle BAD + \angle BCD = 180^\circ \)
- \( \angle ABC + \angle ADC = 180^\circ \)

#### 1. Using the first pair of opposite angles:
\[
\angle BAD + \angle BCD = 180^\circ
\]
\[
(2x - 10) + (5x - 5) = 180
\]
\[
7x - 15 = 180
\]
\[
7x = 195
\]
\[
x = 27.86
\]

#### 2. Using the second pair of opposite angles:
\[
\angle ABC + \angle ADC = 180^\circ
\]
\[
(4x - 10) + (3x + 15) = 180
\]
\[
7x + 5 = 180
\]
\[
7x = 175
\]
\[
x = 25
\]

### Conclusion:
The second calculation is the correct one, so the value of \( x \) is \( 25 \).

However, since the answer choices are different, it might be that a typo exists or further analysis needs to be done. The calculations suggest \( x = 25 \) would be the result for opposite angles based on angle rules. Therefore, none of the provided options match this exactly, but this approach is geometrically sound.

Would you like further details or explanations? Here are 5 related questions for further study:

1. What are the properties of cyclic quadrilaterals in geometry?
2. How can we generalize the angle sum rule for any cyclic quadrilateral?
3. Can we apply similar cyclic quadrilateral principles in 3D geometry?
4. What happens when one angle in a cyclic quadrilateral is a right angle?
5. How do inscribed angles relate to the circle's arc?

**Tip**: Always check for opposite angles in a cyclic quadrilateral, as they sum to 180°.

Diketahui m∠BAD = (2x - 10)°, m∠ABC = (4x - 10)°, m∠BCD = (5x - 5)°, dan m∠ADC = (3x + 15)°. Nilai x yang memenuhi adalah .... derajat

Learn how to solve for x in a cyclic quadrilateral where the angles are expressed as algebraic functions. This problem covers key geometric and algebraic concepts, focusing on the sum of opposite angles in a cyclic quadrilateral.

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