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In triangle PQR, angle Q = 115°. An altitude is drawn from P to the line containing QR. Where does its foot lie?

Class 7The Triangle and its PropertiesTriangles
  • ABetween Q and R, inside the triangle
  • BExactly at the midpoint of QR
  • COn QR produced beyond R
  • DOn RQ produced beyond Q, outside the triangle

Step-by-Step Solution

Angle PQR = 115° is obtuse, so the perpendicular dropped from P cannot land between Q and R — it falls on the extension of RQ past the obtuse vertex Q, outside the triangle. Trap: assuming every altitude lands on the side itself, which is true only for acute triangles; or confusing the altitude with the median, which always ends at the midpoint of QR.
Answer: D) On RQ produced beyond Q, outside the triangle

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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