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In triangle PQR, angle P = 40°. The remaining two angles, angle Q and angle R, are in the ratio 3 : 4. Find angle R in degrees.

Class 7The Triangle and its PropertiesTriangles
  • A80
  • B60
  • C20
  • D70

Step-by-Step Solution

Angle + angle °. Sharing 140° in the ratio 3 : 4 gives 7 parts, so one part = 20°. Then angle ° and angle °. Check: 40 + 60 + 80 = 180. Trap: sharing the full 180° in the ratio instead of the leftover 140°, or stopping at 20° (one part) or 60° (which is angle Q).
Answer: A) 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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