Heya! In the given figure , PQRS is a rhombus and SRM is an equilateral triangle. If SN RM and PRS = 55° , find the size of QSN.

~Thanks in advance!

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:

Step-by-step explanation:

we are given a rombus and an equilateral triangle and

said to figure out

we know that

every angle of an equilateral triangle is 60°

so

should be 60°

the point where two diagonals of triangle bisect be x

recall the diagonals of a rhombus bisect each other at right angles

so should be 90°

we are also given SN RM

so should be 90°

notice that SXRN is a quadrilateral

so the sum of its interior angles is 360°

according to the question

substitute the value of

simplify addition:

cancel 295 from both sides:

hence