Question 162

If PQRS is a rhombus and $$\angle$$SPQ = 50°, then $$\angle$$RSQ is

Solution

Given : $$\angle$$SPQ = 50°

To find : $$\angle$$RSQ = ?

Solution : All sides of a rhombus are equal.

In $$\triangle$$PQS, PQ = PS, => $$\angle$$SPQ = $$\angle$$PQS

=> $$\angle$$PSQ = $$\frac{180^{\circ}-50^{\circ}}{2}$$

=> $$\angle$$PSQ = 65°

Also, diagonals of a rhombus are angle bisectors i.e. $$\angle$$PSQ = $$\angle$$RSQ

=> $$\angle$$RSQ = 65°

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