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In triangle ABC, angle C = 90° and angle A = 32°. Side AB is produced beyond B to a point D. Find angle CBD in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A58
  • B90
  • C148
  • D122

Step-by-Step Solution

Angle B = 180 − 90 − 32 = 58°. Angle CBD is the exterior angle at B, so it equals the sum of the two opposite interior angles: angle A + angle C = 32 + 90 = 122°. Check: 180 − 58 = 122. Trap: giving 58°, which is the interior angle ABC, or 148° (= 180 − 32), which subtracts at the wrong vertex.
Answer: D) 122

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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