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The image shows a quadrilateral \( ABCD \) with diagonal lines intersecting at point \( E \). You are given several angles, and the goal appears to be to find the unknown angle \( x \).

Given the following information:

- \( \angle DAB = 125^\circ \)
- \( \angle ADC = 37^\circ \)
- \( \angle EBD = 51^\circ \)
- \( x = \angle BEC \) (which we are asked to find)

Here’s how we can approach the problem:

1. **Use the properties of the angles in a quadrilateral**: 
   The sum of the interior angles of any quadrilateral is \( 360^\circ \). Hence:
   \[
   \angle DAB + \angle ABC + \angle BCD + \angle CDA = 360^\circ
   \]
   You can calculate \( \angle ABC \) based on this relation.

2. **Investigate triangles for angle sums**: 
   Look at the triangles that could help in solving for \( x \), especially triangle \( EBD \) and triangle \( BEC \). 

I'll go through the necessary calculations to solve for \( x \).The angle \( \angle ABC \) is \( 147^\circ \).

Now, using the fact that triangle \( EBD \) involves angle \( 51^\circ \) (at \( E \)) and the newly found \( \angle ABC \), we can explore the geometry further to calculate \( x \), based on either supplementary or triangle properties.

Let me proceed to calculate \( x \) based on these relations.To calculate the unknown angle \( x \), we need to focus on triangle \( BEC \). Since the diagram involves intersecting diagonals and we have multiple triangles, the next step will depend on understanding any relationships between the known angles.

Here’s an approach:

- In triangle \( BEC \), the angles must sum up to \( 180^\circ \).
- We know that \( \angle EBD = 51^\circ \) and \( \angle ABC = 147^\circ \) is along the exterior line, which suggests that \( \angle EBC \) and \( x \) (which is \( \angle BEC \)) are related by geometry.

However, I will need more details regarding any relationships between the diagonals (whether it's a parallelogram or trapezium) to confirm this.

Would you like me to provide more details on triangle angle sum properties?

The image shows a quadrilateral ABCD with diagonals intersecting at point E. You are asked to find the unknown angle x, given the following angles: ∠DAB = 125°, ∠ADC = 37°, and ∠EBD = 51°.

This problem involves finding the unknown angle x in a quadrilateral ABCD, where diagonals intersect at point E. Given angles include ∠DAB = 125°, ∠ADC = 37°, and ∠EBD = 51°. This problem uses properties of angles in triangles and quadrilaterals. Suitable for students in Grades 9-12.

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