Primary 6 · Angles · Question type 8.7

P6 Angles: Angles in a Folded Figure

A fold changes an angle's position but not its size, so the original and folded angles are equal.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Angles chapter8 question types · see the chapter

The lesson · 2 minutes 10 seconds

How do you solve folded-figure angle questions in P6?

Watch: a rectangle folded along AE, with 58° given

Another worked example

A worked example

PQRS is a piece of paper in the shape of a parallelogram, and angle PQR = 104°. The paper is folded along the line QT, where T is a point on PS, so that the edge QP lies exactly on top of the edge QR. Find angle QTS.

The working · Five lines

The step-by-step working

Written out in full, the way it should appear on paper.

∠PQT = ∠TQR (folded angles are equal)
∠PQT = 104° ÷ 2 = 52° (the two equal angles share ∠PQR)
∠QPT = 180° - 104° = 76° (angles between the parallel sides QR and PS)
∠QTP = 180° - 76° - 52° = 52° (angle sum of triangle PQT)
∠QTS = 180° - 52° = 128° (angles on a straight line PTS)

The answer is 128°.

Practise · Modelled on top school exam questions

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A folded corner

The crease creates equal angles when the corner is folded across it.

ABCD is a rectangular piece of paper. Corner C is folded along the crease BF, where F is on DC. The fold is a wide one: the corner swings right past the edge AB, and C lands at C' outside the paper. Angle C'BF = 58°. Find angle BFC'.

Show the step-by-step solution

∠CBF = ∠C'BF = 58° (folded angles are equal)
∠BFC = 180° - 90° - 58° = 32° (angle sum of triangle BCF)
∠BFC' = ∠BFC = 32° (folded angles are equal)

Ans: 32°

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