Answer:
(a)x=128 degrees
(b)![\angle APD\neq 116^\circ](https://tex.z-dn.net/?f=%5Cangle%20APD%5Cneq%20116%5E%5Ccirc)
Step-by-step explanation:
![\angle ABD+\angle CBD =180^\circ$ (Linear Postulate)\\\angle ABD+116^\circ =180^\circ\\\angle ABD=180^\circ-116^\circ\\\angle ABD=64^\circ](https://tex.z-dn.net/?f=%5Cangle%20ABD%2B%5Cangle%20CBD%20%3D180%5E%5Ccirc%24%20%28Linear%20Postulate%29%5C%5C%5Cangle%20ABD%2B116%5E%5Ccirc%20%3D180%5E%5Ccirc%5C%5C%5Cangle%20ABD%3D180%5E%5Ccirc-116%5E%5Ccirc%5C%5C%5Cangle%20ABD%3D64%5E%5Ccirc)
(a) Now:
![\angle AOD=2 \times \angle ABD$ (Angle at the centre is twice the angle at the circumference)\\x=2 \times 64^\circ\\x=128^\circ](https://tex.z-dn.net/?f=%5Cangle%20AOD%3D2%20%5Ctimes%20%5Cangle%20ABD%24%20%28Angle%20at%20the%20centre%20is%20twice%20the%20%20angle%20at%20the%20circumference%29%5C%5Cx%3D2%20%5Ctimes%2064%5E%5Ccirc%5C%5Cx%3D128%5E%5Ccirc)
(b)
![\angle APD=2 \times \angle ABD$ (Inscribed Angle Theorem)\\\angle APD=2 \times 64^\circ\\ \angle APD=128^\circ](https://tex.z-dn.net/?f=%5Cangle%20APD%3D2%20%5Ctimes%20%5Cangle%20ABD%24%20%28Inscribed%20Angle%20Theorem%29%5C%5C%5Cangle%20APD%3D2%20%5Ctimes%2064%5E%5Ccirc%5C%5C%20%5Cangle%20APD%3D128%5E%5Ccirc)
![\angle APD\neq 116^\circ](https://tex.z-dn.net/?f=%5Cangle%20APD%5Cneq%20116%5E%5Ccirc)
Answer: There is no polygon with the sum of the measures of the interior angles of a polygon is 1920°.
Step-by-step explanation:
The sum of the measures of interior angles of a polygon with
sides is given by:-
![(n-2)\times180^{\circ}](https://tex.z-dn.net/?f=%28n-2%29%5Ctimes180%5E%7B%5Ccirc%7D)
Given: The sum of the measures of the interior angles of a polygon is 1920°.
i.e. ![(n-2)\times180^{\circ}=1920^{\circ}](https://tex.z-dn.net/?f=%28n-2%29%5Ctimes180%5E%7B%5Ccirc%7D%3D1920%5E%7B%5Ccirc%7D)
![n-2=\dfrac{1920}{180}\\\\ n= \dfrac{1920}{180}+2\\\\ n=\dfrac{2280}{180}=12.67](https://tex.z-dn.net/?f=n-2%3D%5Cdfrac%7B1920%7D%7B180%7D%5C%5C%5C%5C%20n%3D%20%5Cdfrac%7B1920%7D%7B180%7D%2B2%5C%5C%5C%5C%20n%3D%5Cdfrac%7B2280%7D%7B180%7D%3D12.67)
But number of sides cannot be in decimal.
Hence, there is no polygon with the sum of the measures of the interior angles of a polygon is 1920°.
Answer:
X=1 9/10
Step-by-step explanation:
6X multiply 2 - 2X=19
Calculate the product
12X-2X=19
Collect the like terms
10X=19
Divide both sides of the equation by 10
X=19/10
Simplify the improper fraction
X=1 9/10
C: scatter plot is the graph used
Answer: 2.5
Step-by-step explanation:
For this problem, we see that 4km is 1/2 of 8km.
So, we will have to find 1/2 of 5km.
1/2 of 5km = 2.5km
Your answer is 2.5km