Given:
In an isosceles triangle LMN, LM=MN.

To find:
The measure of the angles L, M and N.
Solution:
In triangle LMN,
(Given)
(Base angles of an isosceles triangle are equal)
Now,




On further simplification, we get




The value of x is 13. Using this value, we get



Similarly,



And,


Therefore, the measure of angles are
.
Y is equal to 23 and x is equal to 28. This is because you can move 3y over to the corner to its left that matches the position 3y is in. From there you set 3y + 5y -4 = 180 because the add up to a straight line. Then you get 23 for y and you can use that to make 3y=69. Use the 69 to set it equal to 2x +13 and solve to get x=28.
In order to determine the area of the lot of land in squared yards, proceed as follow:
Convert the dimensions of the rectangle to yards, by using the given conversion factor:

Next, consider that the area of the lot is the area of a rectangle. Replace the previous values of the length and the width of the rectangle:

Hence, the area of the lot of land is 656.25 sq yd
Opposite sides are congruent and have the same slope.