Answer:
- The measure of WZ is 16 mm.
Step-by-step explanation:
We know that:
- 2(PR + RS + SP) = WY + YZ + WZ
- PR = 5 mm
- ∠P = 37°
- ∠S = 37°
- PS = 8 mm
- RS = 5 mm
- ΔPRS is an isosceles triangle
- ∠W = 37°
- ∠Z = 37°
- WY = 10 mm
- YZ = 10 mm
- ΔWYZ is an isosceles triangle
We know that both triangles are isosceles because both of them have same angles on the base. Now, let's solve 2(PR + RS + SP) = WY + YZ + WZ.
- 2(PR + RS + SP) = WY + YZ + WZ
- => 2(5 + 5 + 8) = 10 + 10 + WZ [Inserting values]
- => 2(18) = 20 + WZ
- => 36 = 20 + WZ
- => 36 - 20 = WZ
- => 16 mm = WZ
Hence, the measure of WZ is 16 mm.
