Since AB is parallel to DC, ∠C + ∠B = 180°, so ∠B = 90°. ∠N + ∠S = 180°, so ∠S = 180° – 65° = 115°.

Since NE is parallel to SP, ∠N + ∠S = 180°, so ∠S = 180° – 65° = 115°.

Use the correspondence between the angles in ABCD and SPEN.

The angle measures are

∠C = ∠E = 90°

∠B = ∠P = 90°

∠A = ∠S = 115°

∠D = ∠N = 65°

The longest side in ABCD is 12. The longest side in SPEN is 30. Find the scale factor.

^{ABCD}/_{SPEN} = ^{12}/_{30} = ^{2}/_{5}

^{AB}/_{SP} = ^{3}/_{x} = ^{2}/_{5}. SP = 15/2 = 7.5

^{BC}/_{PE} = ^{11}/_{y} = ^{2}/_{5}. PE = 55/2 = 27.5

The perimeter of SPEN is 30 + 7.5 + 27.5 + 20 = 85.

Instead of caclulating CD, use the scale factor to find the perimeter of ABCD.

**The perimeter of ABCD is (2/5)(85) = 34.**