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anonymous

  • one year ago

The measures of three angles of a quadrilateral are 80, 90, and 103 degrees. Find the measure of the fourth angle. A.) 67° B.) 77° C.) 87° D.) 97°

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  1. mathstudent55
    • one year ago
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    The formula for the sum of the angles of a polygon is: \(S = (n - 2)180\) where S = sum of the measures of the angles, and n = number of sides. In this problem, you know you have 4 sides since you have a quadrilateral. Use the formula with n = 4 and find the sum of the measures of the angles. What do you get?

  2. mathstudent55
    • one year ago
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    \(S = (n - 2)180\) \(S = (4 - 2)180\) What do you get for S?

  3. anonymous
    • one year ago
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    Which s?

  4. mathstudent55
    • one year ago
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    In the formula above. S is the sum of the measures of the angles. Just see it below: \(S = (n - 2)180\) \(S = (4 - 2)180 \) What is S equal to?

  5. mathstudent55
    • one year ago
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    First, do 4 - 2. What is 4 - 2?

  6. triciaal
    • one year ago
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    sum of the 4 angles in a quadrilateral = 360 and you have 3

  7. anonymous
    • one year ago
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    2

  8. mathstudent55
    • one year ago
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    Good. Now what is 2 * 180 = ?

  9. anonymous
    • one year ago
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    360

  10. mathstudent55
    • one year ago
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    Great \(S = (4 - 2) 180\) \(S = 2(180) \) \(S = 360\) The sum of the measures of the angles of a quadrilateral is 360.

  11. mathstudent55
    • one year ago
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    We are given the measures of 3 angles. We know the sum of all 4 angles, so we subtract the measure of each angle from 360 to find the missing measure.

  12. mathstudent55
    • one year ago
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    What is: 360 - 80 - 90 - 103 = ? Or you can first add 80 + 90 + 103, and then subtract this sum from 360.

  13. anonymous
    • one year ago
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    87

  14. anonymous
    • one year ago
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    Thank you so much, again!

  15. mathstudent55
    • one year ago
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    Correct. Good job!

  16. mathstudent55
    • one year ago
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    You're welcome.

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