Aplot of land has been surveyed for a new housing development with borders ab, bc, dc, and da. the plot of land is a right trapezoid with a height of 60 feet and an opposite leg length of 65 feet

Thanks that correct

Length of DC= 105 feet.

Explanation:

Given

Right  trapezoid means two angle are of 90 degree.

Draw a perpendicular BE and BE AD .

Length of AB=80 feet

Length of BC=65 feet

Length of AD=60 feet

Length of DC= DE+ EC

Let length of EC= x

Quadrilateral ABED is a parallelogram

ABDE and AB= DE=80 feet

AD= BE=60 feet

Therefore, Length of DC= 80+x

In

By using pythogorous theorem

x=25

Therefore, length of DC= DE+EC=80+25=105 feet .

In quadrilateral ABCD

By usnig property of  sum of angles of quadrilateral

Angle ABC is 119

Length of DC is 105

m∠ABC = 119° and DC = 105 feet

Step-by-step explanation:

For better understanding of the solution see the attached figure of the trapezium ABCD :

m∠BCD = 61°

By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°

⇒ m∠ABC = 180° - 61°

⇒ m∠ABC = 119°

Now, to find length of DC,

Draw a perpendicular BE on CD ⇒ CD = DE + EC

AB = DE

⇒ DE = 80 feet

In ΔBEC, By using Pythagoras theorem

EC² = BC² - BE²

⇒ EC² = 65² - 60²

⇒ EC = 25 feet

Hence, DC = 80 + 25

                   = 105 feet