SOLUTION: Please help me prove the following proof: Given: Quadrilateral ABCD Prove: Measure of angle A + measure of angle B + measure of angle C + measure of angle D = 360 degrees There

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Question 1129844: Please help me prove the following proof:
Given: Quadrilateral ABCD
Prove: Measure of angle A + measure of angle B + measure of angle C + measure of angle D = 360 degrees
There's a diagram that goes with it but i don't know how to show that
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

One way to do this is to split the quadrilateral into two pieces as shown below

Recall that the sum of the three angles of any triangle is always 180 degrees.
For each triangle, we can say
A+B+C = 180
D+E+F = 180
If we add up the two sides of the equations above, then we get
(A+B+C)+(D+E+F) = 180+180
(A+D)+B+(C+F)+E = 360
Which shows that the four angles add up to 360 regardless of what kind of quadrilateral we're working with