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Two angles of a triangle measure 68° and 47°. Classify the triangle by its angles.

Class 7The Triangle and its PropertiesTriangles
  • ARight-angled
  • BObtuse-angled
  • CIt cannot be classified without the side lengths
  • DAcute-angled

Step-by-Step Solution

The third angle is 180 − 68 − 47 = 65°. The angles are 68°, 47° and 65°, all less than 90°, so the triangle is acute-angled. Trap: noticing that 68 + 47 = 115 is more than 90 and calling the triangle obtuse — only a SINGLE angle above 90° makes a triangle obtuse.
Answer: D) Acute-angled

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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