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An exterior angle of a triangle measures 145°. Which pair CANNOT be its two interior opposite angles?

Class 7The Triangle and its PropertiesTriangles
  • A90° and 55°
  • B95° and 60°
  • C72° and 73°
  • D100° and 45°

Step-by-Step Solution

The exterior angle equals the sum of the two interior opposite angles. 90 + 55 = 145, 72 + 73 = 145 and 100 + 45 = 145 all match, but 95 + 60 = 155, which does not. Trap: checking only that each angle is smaller than 145° — every option passes that test; it is the SUM that must equal the exterior angle.
Answer: B) 95° and 60°

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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