Answer:
The measure of angle LMW is 
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc MW
we know that
The inscribed angle measures half that of the arc comprising
so
![m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK]](https://tex.z-dn.net/?f=m%5Cangle%20MLK%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20MW%2Barc%5C%20WK%5D)
substitute the given values
![65\°=\frac{1}{2}[arc\ MW+68\°]](https://tex.z-dn.net/?f=65%5C%C2%B0%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20MW%2B68%5C%C2%B0%5D)
![130\°=[arc\ MW+68\°]](https://tex.z-dn.net/?f=130%5C%C2%B0%3D%5Barc%5C%20MW%2B68%5C%C2%B0%5D)
step 2
Find the measure of arc LK
we know that
-----> by complete circle
substitute the given values
step 3
Find the measure of angle LMW
we know that
The inscribed angle measures half that of the arc comprising
so
![m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK]](https://tex.z-dn.net/?f=m%5Cangle%20LMW%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20LK%2Barc%5C%20WK%5D)
substitute the given values
![m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°](https://tex.z-dn.net/?f=m%5Cangle%20LMW%3D%5Cfrac%7B1%7D%7B2%7D%5B66%5C%C2%B0%2B68%5C%C2%B0%5D%3D67%5C%C2%B0)
Using I = PRT
$2500 - $2000 = $2000 × 0.04 × t
$500 = 80t
t = $500 ÷ 80
t = 6.25 years
so the answer is 6
Answer:
x=-4
Step-by-step explanation:
These two angles have to equal 180 because they are opposite of each other. Therefore, the equation will be 129+x+x+59=180. You add all common terms. 2x+188=180. You want to isolate x so you have to subtract both sides by 188. Therefore, the equation will be 2x=-8. Divide both sides by 2 to isolate x. x=-8/2. This is equal to x=-4.
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The amount of times expected to get a 6 is 5.
30 / 6 = 5
