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To solve for \( x \) in the given diagram, we can make use of the following information:

- We see two triangles and some additional lines. The main triangles to focus on are \( \triangle ADC \) and \( \triangle BDC \).
- From the diagram, \( \angle ADB = 156^\circ \) is given.
- The angles at points \( A \) and \( B \) adjacent to \( D \) are marked as \( a \) and \( b \) respectively.
- These angles at \( A \) and \( B \) are vertically opposite angles at the intersection points and would each equal the corresponding angles on the other side of line \( AB \).

### Step 1: Using angle sum property
The sum of angles in \( \triangle ADC \) is:
\[
\angle A + \angle C + \angle D = 180^\circ
\]

Similarly, in \( \triangle BDC \), the sum of angles is:
\[
\angle B + \angle C + \angle D = 180^\circ
\]

### Step 2: Find \( \angle ADB \)
Since \( \angle ADB = 156^\circ \), the remaining angle at \( D \) inside triangle \( \triangle ADC \) is:
\[
\angle ADC = 180^\circ - 156^\circ = 24^\circ
\]

### Step 3: Relationship between angles \( a \) and \( b \)
Given that the two triangles share the angle \( x \) and each of the angles \( a \) and \( b \) on their opposite sides, we can infer that:
\[
\angle A = 2a, \quad \angle B = 2b
\]

Using these relationships, you can now solve for the unknown \( x \), assuming you can find the values of angles \( a \) and \( b \). Would you like me to proceed with more detailed calculations based on any additional information?

Learn how to find the value of angle x in a geometry problem involving intersecting triangles, with a given angle of 156° at the intersection. This solution involves the angle sum property and vertically opposite angles. Suitable for students in Grades 8-10.

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