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A triangular metal plate has sides 20 cm, 21 cm and 29 cm, and it contains one right angle. Between which two sides does that right angle lie?

Class 7The Triangle and its PropertiesTriangles
  • ABetween the 20 cm and 29 cm sides
  • BBetween the 21 cm and 29 cm sides
  • CBetween the 20 cm and 21 cm sides
  • DThe plate has no right angle

Step-by-Step Solution

, so by the converse of Pythagoras the triangle is right-angled and 29 cm is the hypotenuse. The right angle is always OPPOSITE the hypotenuse, so it lies between the two shorter sides, 20 cm and 21 cm. Trap: making the hypotenuse one arm of the right angle — the hypotenuse faces the right angle, it never forms it.
Answer: C) Between the 20 cm and 21 cm sides

Key idea: Exterior angle property

Extend one side of a triangle past a vertex. The angle formed outside the triangle is the **exterior angle** at that vertex.

**Exterior angle = sum of the two opposite interior angles.**

So if the two non-adjacent interior angles are 50° and 60°, the exterior angle = 50° + 60° = 110°.

Why? The exterior angle and the adjacent interior angle form a linear pair (sum 180°), and the three interior angles also sum to 180°. Subtract: exterior = sum of the other two interior angles.

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