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In triangle ABC, D is a point on side BC. Given angle B = 50° and angle BAD = 30°, find angle ADC in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A100
  • B130
  • C80
  • D20

Step-by-Step Solution

Angle ADC is an exterior angle of triangle ABD at D, so it equals the sum of the two opposite interior angles of that triangle: angle B + angle BAD = 50 + 30 = 80°. Check the long way: angle ADB = 180 − 50 − 30 = 100°, and angle ADC = 180 − 100 = 80°. Trap: answering 100°, which is the adjacent angle ADB, not the one asked for.
Answer: C) 80

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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