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Answer:
Step-by-step explanation:
In the given figure, PQRS is a rhombus and SRM is an equilateral triangle.
We are also given that SN⊥RM and that ∠PRS = 55°.
And we want to find the measure of ∠QSN.
Remember that since PQRS is a rhombus, the angles formed by its diagonals are right angles. Let the intersection point of the diagonals be K. Therefore:
Now, RKS is also a triangle. The interior angles of all triangles must be 180. Thus:
Substitute in known values:
Solve for ∠KSR:
Since SRM is an equilateral triangle, this means that:
Note that RNS is also a triangle. Therefore:
Substitute in known values:
So:
∠QSN is the addition of the two angles:
Therefore: