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In triangle ABC, AB = AC. Side CB is produced beyond B, and the exterior angle formed at B measures 110°. Find angle A in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A70
  • B40
  • C110
  • D55

Step-by-Step Solution

The exterior angle and angle ABC form a linear pair, so angle B = 180 − 110 = 70°. Since AB = AC, the base angles are equal, so angle C = 70° as well. Then angle A = 180 − 70 − 70 = 40°. (Check with the exterior angle property: angle A + angle C = 40 + 70 = 110.) Trap: treating 110° as equal to angle A alone, or stopping at 70°, which is angle B.
Answer: B) 40

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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