quadrilateral wxyz is a rhombus and m<wzx=s+21 what is the value of s?

Answer 1

Since quadrilateral WXYZ is a rhombus, all four angles are equal.

Let's call the measures of all four angles x.

Therefore, m<WZY = m<WXZ = m<ZXY = m<WYX = x.

We know that m<WZX = s + 21.

Since the sum of the angles in a quadrilateral is 360 degrees,

4x = 360.

Dividing both sides by 4, we get:

x = 90.

Therefore, each angle in the rhombus measures 90 degrees.

So, m<WXY = m<XYZ = m<YZW = m<ZWX = 90 degrees.

Since m<WXY = 90, m<WZX = s + 21, substituting 90 for m<WXY, we have:

90 = s + 21.

Subtracting 21 from both sides, we get:

s = 90 - 21 = 69.

Therefore, the value of s is 69.