Question

1. (7 pts) the diagram below is given, where four rays with a common endpoint form four angles with non - overlapping interiors. without drawing anything extra, prove that m∠1 + m∠2 + m∠3 + m∠4 = 360. note: feel free to pop some extra labeled points in the diagram so you can refer to angles easier.

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360 degrees.
Let the common endpoint of the four rays be point O. The four non - overlapping angles ∠1, ∠2, ∠3, and ∠4 are all the angles formed around point O.

Step2: State the conclusion

Since the sum of angles around a point is 360 degrees, we have m∠1 + m∠2 + m∠3 + m∠4=360.

Answer:

m∠1 + m∠2 + m∠3 + m∠4 = 360 is proven by the fact that the sum of angles around a point is 360 degrees.