Solve Quadrilateral Exterior Angles Sum Equal to Interior Angles Sum

  • Thread starter thomasrules
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In summary, the sum of the exterior angles at opposite vertices of any quadrilateral is equal to the sum of the interior angles at the other two vertices. To prove this, you can use the formula 180n-360 for the interior angles and 180n-180(n-2) for the exterior angles. By labeling the four interior angles as A, B, C, and D, and using the fact that A+A'=180 and C+C'=180, you can find the sum of the exterior angles at opposite vertices. This will then equal the sum of the interior angles at the other two vertices.
  • #1
thomasrules
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Prove that the sum of the exterior angles at opposite vertices of any quadrilateral es equal to the sum of the interior angles at the other two vertices.

THIS question is REAly really really really getting me frustrated...

The way we're suppost to do it is like this...

180n-360 is the interior angles and exterior angles is 180n-180(n-2)

From there I don't know...
 
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  • #2
The four interior angles are labeled A, B, C, and D, and you know the sum of these. What happens if you subtract the exterior angles from opposite vertices?
 
  • #3
I don't know man I'm frigging confused...

so you saying that A+B+C+D=360?
 
  • #4
If A and A' are two adjacent angles, then A + A' = 180deg.
Similarly for C and C'. Now find A' + C' wrt A and C. Then find B + D wrt A and C.
 
  • #5
i'm lost :(
 
  • #6
You already know A+B+C+D=360, right?. Now take two opposite angles (assume A and C). What is the sum of the exterior angles of these 2?
 

FAQ: Solve Quadrilateral Exterior Angles Sum Equal to Interior Angles Sum

1. What is the formula for finding the exterior angles of a quadrilateral?

The formula for finding the exterior angles of a quadrilateral is 360 degrees divided by the number of sides. In this case, since a quadrilateral has four sides, the formula would be 360/4 = 90 degrees. This means that each exterior angle of a quadrilateral is 90 degrees.

2. How do you find the sum of the exterior angles of a quadrilateral?

To find the sum of the exterior angles of a quadrilateral, you simply multiply the number of sides by 360 degrees. So in the case of a quadrilateral, the sum of the exterior angles would be 4 x 360 = 1440 degrees.

3. What is the relationship between the exterior angles and interior angles of a quadrilateral?

The exterior angles of a quadrilateral are supplementary to the interior angles. This means that if you add an exterior angle and its corresponding interior angle, the sum will always be 180 degrees. In other words, the exterior angles and interior angles of a quadrilateral are equal.

4. How can you use the exterior angles to find the missing interior angles of a quadrilateral?

If you know the sum of the exterior angles of a quadrilateral (360 degrees) and the measures of some of the exterior angles, you can subtract the known angles from 360 to find the sum of the missing interior angles. From there, you can divide by the number of interior angles to find the measure of each angle.

5. Can you use the exterior angles to determine if a quadrilateral is regular or irregular?

Yes, you can use the exterior angles to determine if a quadrilateral is regular or irregular. In a regular quadrilateral, all four exterior angles will be equal (90 degrees). In an irregular quadrilateral, the exterior angles will have different measures.

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