Question

A plot 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. If the measure of angle BCD is 61, the measure of angle ABC is If the length of base AB is 80 feet, the length of DC is feet.

Answer 1

Angle ABC is 119

Length of DC is 105

Answer 2

`\angle ABC=119^(\circ)`

Length of DC= 105 feet.

Step-by-step explanation:

Given
`\angle BCD=61^(\circ)`

Right trapezoid means two angle are of 90 degree.

`\angle BAD=90^(\circ)`

`\angle ADC=90^(\circ)`

Draw a perpendicular BE and BE
`\parallel` 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

`\therefore` AB
`\parallel`DE and AB= DE=80 feet

AD= BE=60 feet

Therefore, Length of DC= 80+x

In
`\triangle BEC`

`BE^2+EC^2=BC^2`

By using pythogorous theorem

`x^2+ (60)^2= (65)^2`

`x^2+3600=4225`

`x^2=625`

`x=√(625)`

x=25

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

In quadrilateral ABCD

`\angle ABC+\angle BCD+\angle ADC+\angle BAD=360^(\circ)`

By usnig property of sum of angles of quadrilateral

`\angle ABC+61+90+90= 360`

`\angle ABC= 360-241`

`\angle ABC=119^(\circ)`