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In triangle ABC, angle B = 90°. A point D lies on BC and AD is joined, with angle BAD = 25° and angle DAC = 30°. Find angle C in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A65
  • B35
  • C55
  • D60

Step-by-Step Solution

Angle BAC = angle BAD + angle DAC = 25 + 30 = 55°. In triangle ABC, angle C = 180 − 90 − 55 = 35°. Trap: staying inside triangle ABD and giving 65° (= 90 − 25), which is angle ADB, or reporting 55°, which is angle A itself.
Answer: B) 35

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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