Explain what you see in this diagram using only words, without any calculations. How would you work out each angle, if only angle 1 was given and the two horizontal lines are parallel to each other?

The diagram shows two parallel horizontal lines intersected by a diagonal transversal line and a vertical transversal line. The intersections create 16 numbered angles. A square symbol indicates that the vertical line is perpendicular to the top horizontal line.

Here's how to work out each angle if only angle 1 is given:

• Angles 2, 3, 4:

  • Angle 2 is found by subtracting angle 1 from $180^\circ$ because they form a linear pair (angles on a straight line).
  • Angle 3 is equal to angle 1 because they are vertically opposite angles.
  • Angle 4 is equal to angle 2 because they are vertically opposite angles.

• Angles 5, 6, 7, 8:

  • Angle 5 is equal to angle 1 because they are corresponding angles (formed by parallel lines and a transversal).
  • Angle 6 is equal to angle 2 because they are corresponding angles.
  • Angle 7 is equal to angle 1 because they are alternate interior angles.
  • Angle 8 is equal to angle 2 because they are alternate interior angles.

• Angles 9, 10, 11, 12:

  • The square symbol indicates that the angle formed by the vertical line and the top horizontal line is $90^\circ$. This means angles 10 and 11 are both $90^\circ$.
  • Angles 9 and 12 are also $90^\circ$ because they are supplementary to angles 10 and 11 respectively, or vertically opposite to angles 11 and 10.

• Angles 13, 14, 15, 16:

  • Since the two horizontal lines are parallel and the vertical line is perpendicular to the top horizontal line, it must also be perpendicular to the bottom horizontal line. Therefore, angles 13, 14, 15, and 16 are all $90^\circ$.