Topics › Geometry › Q147
Folding · equal angles
P6 · Geometry · PSLE Maths
Question
Mei Ling made a rectangular bookmark ABCD, where AB ∥ CD. She folded the bookmark along the line EF, meeting AB at E and CD at F. After the right part was folded to the left, the image of the original top edge EB lies on line EG and meets CD at G. Given that ∠EFG = 52°, find ∠EGF = x.
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Hint
First use parallel lines to find the angle between EB and EF before folding, then use the fact that angles before and after folding are equal.
Show the answer and step-by-step explanation
Answer: ∠EGF 76° °
- Read the diagram — First draw the bookmark. AB and CD are the top and bottom sides of a rectangle, so they are parallel. EF is the crease, and EG is the folded top edge.
- Use parallel lines — Since AB ∥ CD, the top edge EB is parallel to the bottom edge GF. So the 52° made by EF with the bottom edge is also the angle made by EF with the original top edge EB.
- Equal by folding — The crease EF acts like a mirror. Before folding, EB makes a 52° angle with EF. After folding, EG makes the same angle with EF, so it is also 52°.
- Look at the triangle — Now look at triangle EFG. We already know two angles: 52° and 52°. The angles in a triangle add up to 180°.
- Find x — Calculate: 180° − 52° − 52° = 76°. So ∠EGF = 76°. 📌 Key idea: in folding questions, first use parallel-line angles, then use equal angles about the crease, and finally use the angle sum of a triangle.
Method: The top and bottom sides of a rectangle are parallel, so use corresponding or alternate angles. The fold line acts like a mirror, so the angle made with the crease before folding equals the angle after folding.
Practice: 3 similar questions
- Raju has a rectangular strip PQRS, where PQ ∥ SR. He folds it along MN, with M on PQ and N on SR. After folding, the original MQ lies on MT and meets SR at T. Given that ∠MNT = 48°, find ∠MTN.
Answer
84° ° — Since PQ ∥ SR, the angle between the crease MN and the top edge MQ equals ∠MNT = 48°. The angles made with the crease before and after folding are equal, so ∠TMN = 48°. In triangle MTN, ∠MTN = 180° − 48° − 48° = 84°.
- Siti folds a rectangular gift tag. The crease AB makes a 63° angle with the bottom edge at B. After folding, the image of the top edge AC meets the bottom edge at C. Find the angle ∠ACB formed at C.
Answer
54° ° — The top and bottom edges of the rectangle are parallel, so the angle between the crease and the original top edge is 63°. After folding, the angle between the crease and the folded edge is still 63°. In triangle ABC, ∠ACB = 180° − 63° − 63° = 54°.
- Ali folds a rectangular strip. The crease EF makes an angle of a° with the bottom edge. After folding, the image of the top edge EG meets the bottom edge at G and forms angle x. Given that x is equal to a, find x.
Answer
60° ° — By parallel lines and equal folding angles, two angles in the triangle are both a°. So 2a + x = 180. Also, x = a. Substitute: 2a + a = 180, so 3a = 180 and a = 60. Therefore, x = a = 60°.
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