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Given ∠P = 70° Diagonals PR = 9 cm and QS = 8cm We know that the diagonals are perpendicular to each other. So we have right angle triangles Let the diagonals meet each other at O. Then PO = 1/2 PR = 9/2 = 4.5 cm And QO = 1/2 QS = 8/2 = 4 cm We have ΔPOQ, in ΔPOQ PQ is the hypotenuse According to the pythagoras theorem PQ² = PO² + QO² ⇒PQ² = 4.5² + 4² ⇒PQ² = 20.25 + 16 ⇒PQ² = 36.25 ⇒PQ = √36.25 ∴ PQ = 6.02 cm Side of the rhombus = 6.02 cm Perimeter = 4(6.02) = 24.08 cm Opposite angles are equal in a rhombus ∴∠P = ∠R ∴∠R = 70° And ∠Q = ∠S ----------(1) In a rhombus adjacent angles are supplementary ∴∠P + ∠Q = 180° 70° + ∠Q = 180° ∠Q = 180° - 70° ∴∠Q = 110° From (1) ∠Q =∠S =110° ∴The angles are 70°, 110°, 70°, 110°