Triangle ABC is equilateral. Point D lies on side AB and point E lies on side BC, and the straight line DE joins them. ∠BDE = 74°.
- Find ∠DEB.
- Find ∠CED.
Need a hint?
Use the angle sum of triangle DBE first, then the straight line BEC at E.
Worked answer
- ∠DBE = 60° because triangle ABC is equilateral.
- (a) In triangle DBE: ∠DEB = 180° − 60° − 74° = 46°.
- (b) B, E and C lie on a straight line, so ∠CED = 180° − 46° = 134°.
Answer: 134 °
The mistake this question tests
Habit
Angle facts (straight line, triangle, quadrilateral)
Pupils give 46° for (a) because they read ∠DEB instead of its supplement ∠CED, which lies on the straight line BEC.
How to fix it at home →Wrong answers children often give:
- 46° Angle facts (straight line, triangle, quadrilateral)
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