Vidya has just opened her book. Let us observe her opening the cover of the book in different scenarios (Case 1 to Case 6). Do you see angles being made in each of these cases? Can you mark their arms and vertex?
Answer
Yes — an angle is formed in every case.
The vertex is the spine of the book, the fixed edge about which the cover turns.
The two arms are the cover of the book and the page (or table) lying flat underneath it.
An angle: two rays BD and BE from the common starting point B. B is the vertex; BD and BE are the arms.
Why: an angle is made by two rays that start from the same point. The spine is that common starting point; the cover and the base sheet act like two rays going out from it. As the cover is lifted, only the amount of turn changes — so the angle grows while the arms stay the same length.
Q2.
Which angle is greater—the angle in Case 1 or the angle in Case 2?
Answer
The angle in Case 2 is greater.
To reach Case 2, Vidya has to rotate the cover more than she did for Case 1.
Case 1 < Case 2 < Case 3 < Case 4 < Case 5 < Case 6
The big idea: just as the size of a line segment is measured by its length, the size of an angle is measured by the amount of rotation needed about the vertex to move the first ray onto the second ray. More turn means a bigger angle.
Q3.
In a compass or divider, we turn the arms to form an angle... A pair of scissors has two blades... Look at the pictures of spectacles, wallet and other common objects. Identify the angles in them by marking out their arms and vertices.
Answer
Every one of these objects has a hinge — and a hinge is a vertex.
Object
Vertex (fixed point)
Arms of the angle
Compass / divider
the screw joining the two legs
the two legs
Scissors
the rivet at the centre
the two blades
Spectacles
the hinge near each glass
the frame and the side arm
Wallet / book
the fold or the spine
the two flaps or covers
Door
the hinge on the frame
the door and the wall
Why they are all angles: in each object one part is turned with respect to the other about a fixed point. That turning is exactly what an angle measures.