Given: KLMN is a trapezoid, KL = MN,

Question

m∠1=m∠2, LM:KN = 8:9 , PKLMN = 132
Find: The length of the legs.

I got 49, but it was wrong

Answer 1

You have not made it clear what ∠1 and ∠2 are. Try using letters, such as

∠1 = ∠KNM or something

Also, which sides are the parallel bases? If they are KL and MN, then the figure is a parallelogram.

Is PKLMN the perimeter? Or is P some other point outside the trapezoid.

You need to remember that we cannot see the diagram, so it is not always obvious just where thing are.

Answer 2

P stands for the perimeter, and LM and KN are parallel. angle one is LKM and angle 2 is MKN

Answer 3

I had this question too, and the lines LM and KN are parallel, that means m∠2 is congruent to angle LMK due to alternate interior angles. Since m∠1=m∠2, the triangle LMK would be isosceles due to base angle theorem converse. So LM would be congruent to LK and MN (def. of isosceles triangle) which is 8x. So then 8x+8x+8x+9x=132 and I think you can figure it out from there.
Hope this helps.

Answer 4

Ok so we know that KL = MN which is given and then <1 = <2 which is congruent to <KML. Triangle KLM is also an isosceles triangle. <M = 8x = KL. so label legs KL and MN with 8x and also base LM with 8x. KN is 9x because of the ratio given 8/9 just make it 8x and 9x. Just like the person above said earlier, then add to find perimeter so 8x + 8x+8x+9x = 132, which gives you x = 4. To find the length of the midsegment you add the bases and divide by two so top base 8x is 8(4) = 32. The bottom base would be 9x = 9(4)=36. FINALLY, you have (34 + 36)/2 which gives you 34!!