How to draw angles - Euclid

“So how many degrees are there in a triangle?” Asked Euclid’s friends. “Well,” said Euclid. “You remember how I turned a circle into a square using a piece of string?” “Oh yes! We liked that.” Euclid’s friends cheered. “We liked that a lot!” “You would think that the same thing would work for a triangle, but it doesn’t. This is how you can prove it.” Euclid drew a square and wrote 90 in each corner. “You will remember,“ he said, “that a square has four corners. Each corner is a right angle, and a right angle is 90 degrees. Four times 90 adds up to 360 degrees which is the same as a circle. “Yes! We remember all that!” Euclid’s friends grumbled, impatiently. “Draw a line from one corner of the square, across the middle, to the other corner. This line is called the Diagonal. It cuts the square in half diagonally. Now what have we got?” Euclid’s friends stared at the drawing. “Two triangles!” they exclaimed. Euclid smiled to himself. “In each triangle there is one right angle and two right angles that have been cut in half. A half of 90 degrees is 45, so 90 plus 45 plus 45 equals…” “180!” Euclid’s friends cheered. “There you are,” said Euclid. “The inside angles of a triangle always add up to 180 degrees. Quad Erat Demonstrandum! as the Roman’s would say.” “But we’re ancient Greeks!” said Euclid’s friends. “We certainly are!” said Euclid, enigmatically.