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Mathematics

In rhombus PQRS; A, B and C are mid-points of sides PQ, QR and RS respectively. If ∠P = 60°, the angle PQR is equal to:

In rhombus PQRS; A, B and C are mid-points of sides PQ, QR and RS respectively. If ∠P = 60°, the angle PQR is equal to: Mid-Point Theorem, Concise Mathematics Solutions ICSE Class 9.

  1. 60°

  2. 90°

  3. 120°

  4. none of these

Mid-point Theorem

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Answer

Given, ∠P = 60°

∠P and ∠PQR are consecutive angles in the rhombus.

The sum of consecutive angles in a rhombus is 180°.

⇒ ∠P + ∠PQR = 180°

⇒ 60° + ∠PQR = 180°

⇒ ∠PQR = 180° - 60°

⇒ ∠PQR = 120°.

Hence, option 3 is the correct option.

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