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One angle of a triangle measures 95°. Which statement about this triangle MUST be true?

Class 7The Triangle and its PropertiesTriangles
  • AIt cannot be right-angled.
  • BIt cannot be isosceles.
  • CIts other two angles add up to 95°.
  • DIt must be scalene.

Step-by-Step Solution

95 + 90 = 185, which already exceeds 180, so a second angle of 90° is impossible and the triangle cannot be right-angled. It CAN be isosceles (95°, 42.5°, 42.5°), so it need not be scalene, and the other two angles sum to 180 − 95 = 85°, not 95°. Trap: reading the 95° as the amount left over rather than the amount already used up.
Answer: A) It cannot be right-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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