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Which pair of descriptions can never apply to the same triangle?

Class 7The Triangle and its PropertiesTriangles
  • AObtuse-angled and isosceles
  • BRight-angled and isosceles
  • CAcute-angled and scalene
  • DObtuse-angled and equilateral

Step-by-Step Solution

Every equilateral triangle has three 60° angles, so it can never contain an angle greater than 90°. The other three all exist: 120°, 30°, 30° is obtuse isosceles; 90°, 45°, 45° is right isosceles; 50°, 60°, 70° is acute scalene. Trap: assuming "equilateral" restricts only the sides — equal sides force equal 60° angles too.
Answer: D) Obtuse-angled and equilateral

Key idea: Angle sum property

**The three interior angles of any triangle sum to 180°.**

This is true for every triangle — equilateral, isosceles, scalene, right, acute, or obtuse. Use it to find a missing angle when you know the other two: third angle = 180° − (first) − (second).

Special cases:
- Equilateral: all angles equal → each is 60°.
- Right triangle: one is 90°, so the other two sum to 90° (they are complementary).

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