anonymous
  • anonymous
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°
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
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?
mathstudent55
  • mathstudent55
\(S = (n - 2)180\) \(S = (4 - 2)180\) What do you get for S?
anonymous
  • anonymous
Which s?

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More answers

mathstudent55
  • mathstudent55
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?
mathstudent55
  • mathstudent55
First, do 4 - 2. What is 4 - 2?
triciaal
  • triciaal
sum of the 4 angles in a quadrilateral = 360 and you have 3
anonymous
  • anonymous
2
mathstudent55
  • mathstudent55
Good. Now what is 2 * 180 = ?
anonymous
  • anonymous
360
mathstudent55
  • mathstudent55
Great \(S = (4 - 2) 180\) \(S = 2(180) \) \(S = 360\) The sum of the measures of the angles of a quadrilateral is 360.
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
What is: 360 - 80 - 90 - 103 = ? Or you can first add 80 + 90 + 103, and then subtract this sum from 360.
anonymous
  • anonymous
87
anonymous
  • anonymous
Thank you so much, again!
mathstudent55
  • mathstudent55
Correct. Good job!
mathstudent55
  • mathstudent55
You're welcome.

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