Calculate, without giving reasons, the value of x in each of the following.

Here are the completed statements and calculations:

Worksheet 13 B

12. $\angle 3 = \angle 7$, because they are corresponding angles and AB || CD.
13. $\angle 5 = \angle 7$, because they are vertically opposite angles.
14. $\angle 1 = \angle 5$, because they are corresponding angles and AB || CD.
15. $\angle 4 = \angle 5$, because they are alternate angles and AB || CD.
16. $\angle 3 + \angle 5 = 180^\circ$, because they are co-interior angles and AB || CD.
17. $\angle 5 + \angle 6 = 180^\circ$, because they are adjacent angles on a straight line EF.
18. $\angle 5 + \angle 8 = 180^\circ$, because they are adjacent angles on a straight line CD.
19. $\angle 1 + \angle 2 + \angle 3 + \angle 4 = 360^\circ$, because they are adjacent angles around a point (revolution).
20. $\angle 5 + \angle 6 + \angle 7 + \angle 8 = 360^\circ$, because they are adjacent angles around a point.

Worksheet 13 C

5. The angles $x$ and $128^\circ$ are angles on a straight line, so their sum is $180^\circ$.

   $$x + 128^\circ = 180^\circ$$ $$x = 180^\circ - 128^\circ$$ $$x = \boxed{\text{52}^\circ}$$

6. The angle $x$ and the right angle ($90^\circ$) are vertically opposite angles. Vertically opposite angles are equal.

   $$x = \boxed{\text{90}^\circ}$$

7. The $40^\circ$ angle and the angle corresponding to $x$ are supplementary. The angle corresponding to $40^\circ$ (exterior, upper-left) is the exterior angle in the lower-left position. Let's call this angle $y$. So $y = 40^\circ$. The angles $x$ and $y$ are consecutive exterior angles, which are supplementary.

   $$x + 40^\circ = 180^\circ$$ $$x = 180^\circ - 40^\circ$$ $$x = \boxed{\text{140}^\circ}$$

8. The angles $5x$ and $130^\circ$ are alternate interior angles. Since the lines are parallel, alternate interior angles are equal.

   $$5x = 130^\circ$$ $$x = \frac{130^\circ}{5}$$ $$x = \boxed{\text{26}^\circ}$$