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In triangle ABC, angle C = 80° and angle A is 20° more than angle B. Find angle B in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A50
  • B60
  • C40
  • D30

Step-by-Step Solution

Angle A + angle . With angle = angle → → angle °, so angle °. Check: 60 + 40 + 80 = 180. Trap: splitting the leftover 100° evenly gives 50° each and ignores the 20° gap; 60° answers for angle A, not angle .
Answer: C) 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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