In a cyclic quadrilateral, the opposite angles add up to 180 degrees.
Opposite angle to angle A = Angle D.
A + D = 180
64 + D = 180
D = 180 - 64
D = 116°
Option E.
They are supplementary angles. They are located on a straight line, and when added together they will add up to 180 degrees.
Step-by-step explanation:
Since no other info is given, you would use a protractor, centered at O. Read off the degree measure, to the nearest degree (a high quality protractor may have divisions to a quarter of a degree). Arc AC has that many degrees.
If the angle is ABC, where B is also on the circle, this is called an inscribed angle, with vertex (its”point”) at B. Now, arc AC will have exactly twice the degree measure of angle ABC. That is a theorem in geometry textbooks, which has been known for about 2500 years!
Answer:
![m=8.6464\ Kg](https://tex.z-dn.net/?f=m%3D8.6464%5C%20Kg)
Step-by-step explanation:
step 1
Find the volume of the trapezoidal prism
The volume of the prism is equal to
![V=BL](https://tex.z-dn.net/?f=V%3DBL)
where
B is the area of the trapezoidal face
L is the length of the prism
Find the area of the base B
we know that
The area of a trapezoid is equal to
![B=\frac{1}{2}[6+10](4)=32\ cm^2](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B1%7D%7B2%7D%5B6%2B10%5D%284%29%3D32%5C%20cm%5E2)
we have
![L=14\ cm](https://tex.z-dn.net/?f=L%3D14%5C%20cm)
substitute
![V=32(14)=448\ cm^3](https://tex.z-dn.net/?f=V%3D32%2814%29%3D448%5C%20cm%5E3)
step 2
Find the mass
Remember that
The density is equal to divide the mass by the volume
so
![D=\frac{m}{V}](https://tex.z-dn.net/?f=D%3D%5Cfrac%7Bm%7D%7BV%7D)
we have
![D=19.3\ g/cm^3](https://tex.z-dn.net/?f=D%3D19.3%5C%20g%2Fcm%5E3)
![V=448\ cm^3](https://tex.z-dn.net/?f=V%3D448%5C%20cm%5E3)
substitute
![19.3=\frac{m}{448}](https://tex.z-dn.net/?f=19.3%3D%5Cfrac%7Bm%7D%7B448%7D)
solve for the mass
![m=19.3(448)=8,646.4\ g](https://tex.z-dn.net/?f=m%3D19.3%28448%29%3D8%2C646.4%5C%20g)
Convert to Kg
Remember that
![1\ Kg=1,000\ g](https://tex.z-dn.net/?f=1%5C%20Kg%3D1%2C000%5C%20g)
therefore
![m=8.6464\ Kg](https://tex.z-dn.net/?f=m%3D8.6464%5C%20Kg)