Naming and measuring angles

The figure shows two rays, B A and B C, meeting at B. Use a protractor to measure angle A B C. Try it first. Pause if you like. Which letter is the vertex? Which arm will the protractor baseline follow? The arms B A and B C meet at B, so the centre mark goes on B. B is the middle letter in angle A B C. Reversing the outer letters gives angle C B A, the same opening. Place the protractor centre mark exactly on B. Keep the centre on B while turning the baseline onto B A. The angle on the paper stays still. Step one: position the protractor so that the baseline is along B A, with the centre mark on B. The arms stop before the scale. Extend them along their own straight directions so we can read the protractor easily. Find zero on B A. This inner scale starts there. The other scale runs the opposite way. Step two: read the scale whose zero mark is on B A. Follow that scale from zero towards B C. Each small tick marks one degree. B C meets the scale two small ticks after sixty. The reading is sixty-two degrees. This opening is smaller than a right angle, so a reading below ninety degrees makes sense. Find the vertex, line up the baseline, then read the scale that starts at zero on that arm.

Three rays, T U, T V and T W, leave T. Use a protractor to measure angle V T W. Try it first. Pause if you like. There are three arms. Which two belong to the angle named in the question? In angle V T W, the middle letter is T, so T is the vertex. The outer letters are V and W, so the arms are T V and T W. T U is not part of this angle. Place the protractor centre mark on T. Turn its baseline onto T W, keeping the centre fixed on T. Step one: position the protractor with the baseline along T W and the centre mark on T. Extend T W and T V along their straight directions until they reach the scale. Use the zero mark on T W to choose the scale. Step two: read the scale whose zero mark is on T W. Follow that scale from zero towards T V. Ignore the third arm. T V crosses two small ticks before forty, at thirty-eight degrees. The middle letter finds the vertex. The outer letters choose the arms. The zero on the baseline chooses the scale.