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Anarel [89]
3 years ago
13

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 trap

ezoid 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.
Answers are 119, and 105 on e2020

Mathematics
2 answers:
sdas [7]3 years ago
3 0

Answer:

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

vekshin13 years ago
3 0

Answer: Thanks that correct



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