Solved Examples & Common Mistakes

Mind the Mistake (Protractor Errors)

Students often make mistakes when reading a protractor. Let’s analyze the errors from Page 32.

Case 1: $\angle U = 35^\circ$?

Mistake: The student placed the baseline on the edge of the protractor plastic, not the $0^\circ$ line. Correction: Align the arm of the angle exactly with the $0^\circ$ - $180^\circ$ line.

Case 2: $\angle V = 80^\circ$?

Mistake: The vertex of the angle is NOT at the center point of the protractor. Correction: Place the center of the protractor’s base exactly on the vertex.

Case 3: $\angle W = 70^\circ$?

Mistake: Reading the wrong scale. The angle is obtuse (wide), but $70^\circ$ is acute. Correction: Read the scale that starts at $0^\circ$ on the side of the arm. The correct measure is $110^\circ$.

Case 4: $\angle Z = 85^\circ$?

Mistake: The baseline is not aligned with either arm. Correction: Rotate the protractor so the $0^\circ$ line lies flat on one of the arms.

Triangle Angle Sum Conjecture

Experiment: If you measure the three angles of any triangle (like in Page 31), and add them up, what do you get?

Result: You will find the sum is always very close to or exactly $180^\circ$.