Topics › Geometry › Q155
Parallel lines and angles in triangles
P6 · Geometry · PSLE Maths
Question
Ali is making a trapezium frame ABCD for the class notice board. AB // DC, and diagonal BD is drawn. Given that ∠ABD = 38° and ∠BCD = 112°, find ∠CDB.
Try it yourself · watch the animation →
Hint
First use AB // DC to find the co-interior angle ∠ABC, then see which two angles ∠ABC is split into by BD.
Show the answer and step-by-step explanation
Answer: ∠CDB 38 °
- Read the diagram — This is trapezium ABCD, with AB // DC. Diagonal BD splits the angle on the right into smaller angles.
- Co-interior angles — Since AB // DC, BC is a transversal. So the co-interior angles ∠ABC + ∠BCD = 180°.
- Split the angle — At B, ∠ABC = 68°. It is split by BD into 38° and ∠DBC.
- Angle sum of triangle — Now look at triangle BCD. Its three interior angles add up to 180°: ∠BCD = 112° and ∠DBC = 30°, so we can find ∠CDB.
- Answer — Therefore, ∠CDB = 38°. 📌 Key idea: use parallel lines for co-interior angles, split the larger angle, then use the angle sum of a triangle.
Method: Co-interior angles in parallel lines add up to 180°. Split the larger angle into smaller angles, then use the angle sum of a triangle, 180°, to find the unknown angle.
Practice: 3 similar questions
- In trapezium ABCD, AB // DC, and diagonal BD is drawn. Given that ∠ABD = 45° and ∠BCD = 105°, find ∠CDB.
Answer
45 ° — Since AB // DC, ∠ABC + ∠BCD = 180°. So ∠ABC = 180° − 105° = 75°. ∠DBC = ∠ABC − ∠ABD = 75° − 45° = 30°. In triangle BCD, ∠CDB = 180° − 105° − 30° = 45°.
- Siti drew a trapezium ABCD with AB // DC and joined BD. Given that ∠ABD = 32° and ∠BCD = 116°, find ∠CDB.
Answer
32 ° — ∠ABC = 180° − 116° = 64°. ∠DBC = 64° − 32° = 32°. In triangle BCD, ∠CDB = 180° − 116° − 32° = 32°.
- Raju drew diagonal BD in trapezium ABCD, where AB // DC. Given that ∠BCD = 124° and ∠CDB = 41°, find ∠ABD.
Answer
41 ° — In triangle BCD, ∠DBC = 180° − 124° − 41° = 15°. Since AB // DC, ∠ABC = 180° − 124° = 56°. ∠ABD = ∠ABC − ∠DBC = 56° − 15° = 41°.
Learn it on classai
An animation walks through each step, then 3 similar questions check it stuck; mistakes come back for review after 1, 3 and 7 days.
Open this question →