What is the solution to finding the angle in this geometry homework problem?

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To find the angle in the geometry problem, the correct approach involves using the formula for angles outside a circle, which states that the angle equals half the difference of the intercepted arcs. The initial calculation mistakenly applied the formula for angles inside the circle. The correct setup involves determining the intercepted arcs accurately, leading to the equation 70 = 0.5(40 + x). The resulting value for x should be adjusted based on this formula to find the correct angle. The key takeaway is to ensure the appropriate formula is applied based on the angle's position relative to the circle.
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Homework Statement


See the attachment

The Attempt at a Solution


Is the answer simply 70-40=30?
 

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You're trying to find angle 1, right? It looks to me like you are given that it is 40 degrees.
 
I'm pretty sure 40 degrees refers to that arc of the circle. In this case, you need two formulas:

1) Angle inside circle equals one-half of the sum of the intercepted arcs.
2) Angle outside circle equals one-half of the difference of the intercepted arcs.
 
70 = .5 (40+x)
x = 100

Angle 1 = .5(100+40)
Angle 1 = 70

However this answer is not an option. Where is my mistake?
 
Last edited:
golb0016 said:
Angle 1 = .5(100+40)

Your mistake is in this line. The angle outside the circle is equal to half the difference of the intercepted arcs.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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