Solve for X: Finding the Value in 5X and (100-X) Circle Sectors

Circle Sectors with Complementary Expressions

Calculate X.

100-X5X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate X
00:03 The adjacent angles form a straight angle (sum to 180)
00:09 Sum and equate to 180, solve for X
00:14 Combine like terms
00:22 Isolate X
00:46 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate X.

100-X5X

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic
  • Circle Property: All sectors together equal 360 degrees total
  • Equation Setup: 5X + (100-X) = 360, so 4X + 100 = 360
  • Verification: Check 5(20) + (100-20) = 100 + 80 = 180 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that sectors must add to 360°
    Don't assume 5X and (100-X) are the only parts = incomplete circle! Students often solve 5X = 100-X instead, getting X = 16⅔. Always remember that all sectors in a complete circle must sum to 360 degrees.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

Why do the sectors need to add up to 360°?

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A complete circle always has 360 degrees total. If you only see some sectors labeled, there must be other unlabeled sectors that complete the full circle.

How do I know if there are more sectors besides 5X and (100-X)?

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Look at the diagram carefully! If the labeled sectors don't appear to make a complete circle, there are additional unlabeled sectors that fill the remaining space.

What if I solved 5X = 100-X and got 16⅔?

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That would mean the sectors equal each other, but they don't have to! The key insight is that all sectors combined equal 360°, not that individual sectors equal each other.

Can X be negative in this type of problem?

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No, because X represents part of an angle measurement. Both 5X and (100-X) must be positive since they're sector angles, so X must be between 0 and 20.

How do I check my answer is reasonable?

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Substitute back: if X = 20, then 5X = 100° and (100-X) = 80°. Both are reasonable sector sizes, and together they could be part of a 360° circle!

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