The folded triangle and the angle that doubles
Where to find it
This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2017 Paper 2, Q17, parts (a) and (b) (the folded-triangle angles question) — then follow our worked solution below.
The lock
Children know angles in a triangle sum to 180°, but a fold reflects an angle to a new place, and the reflected angle is easy to put in the wrong spot. Treat the fold as a mirror.
The key
Find the base angles first, then track each reflected angle to its true position.
Worked steps
- Base angles of the isosceles triangle: angle BAC = angle BCA \(= (180^\circ - 84^\circ) \div 2 = 48^\circ\).
- (a) In triangle DEC, angle \(x = 180^\circ - 48^\circ - 67^\circ = 65^\circ\) (the fold reflects this angle to where \(x\) is marked).
- (b) The fold places a second 67° beside the first at D, so the straight line at D leaves \(180^\circ - 67^\circ - 67^\circ = 46^\circ\) for the folded edge.
- In the small triangle at A, angle \(y = 180^\circ - 48^\circ - 46^\circ = 86^\circ\).
Answer: (a) x = 65°. (b) y = 86°.
What makes it click. A fold is a mirror, nothing more. The 67° appears twice, the base angle 48° travels along, and angle-chasing does the rest. Drawing the reflected angle in its true position is the whole battle.
Independently solved, matches the GPA marking-scheme key. Open the full worked solution →