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We are given a geometric diagram with three straight lines \( DAC \), \( FCB \), and \( ABE \), along with specific angles. The goal is to determine the value of the angle marked \( x \).

### Steps to solve for \( x \):

1. **Straight Line Rule**: The angle on a straight line sums to \( 180^\circ \).
   - Angle \( \angle FCB = 135^\circ \) is given.
   - Therefore, \( \angle ACB = 180^\circ - 135^\circ = 45^\circ \).

2. **Triangle Angle Sum**: The sum of angles in a triangle is always \( 180^\circ \). In triangle \( ACB \):
   \[
   \angle ACB + \angle BAC + \angle ABC = 180^\circ
   \]
   Substituting the known values:
   \[
   45^\circ + 70^\circ + x = 180^\circ
   \]
   Simplifying:
   \[
   115^\circ + x = 180^\circ
   \]
   \[
   x = 180^\circ - 115^\circ = 65^\circ
   \]

Therefore, the value of the angle marked \( x \) is \( 65^\circ \).

Would you like any further clarification or details?

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Here are 5 related questions to expand on this problem:
1. How would the solution change if one of the given angles was different?
2. Can you prove why the sum of angles in any triangle is always \( 180^\circ \)?
3. What is the relationship between exterior angles and interior angles of a triangle?
4. How would you approach solving for an unknown angle in a non-right triangle?
5. Can this method be applied to a quadrilateral? Why or why not?

**Tip**: Always remember to check that the diagram follows the rules for angles on straight lines and triangles. It helps in verifying your answers!

DAC, FCB, and ABE are straight lines. Work out the size of the angle marked x. You must give reasons for your answer. Given angles are 70°, 135°.

Learn how to calculate the unknown angle x in a geometric problem involving straight lines and triangles. The problem includes concepts such as the sum of angles in a triangle and angles on a straight line. Suitable for Grades 7-9.

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