Question

50 POINTS! Fully correct and explanatory answers only!

In the figure, ∠4 is an exterior angle to triangle ∠A∠U∠L .



(a) What is the angle measurement of Angle 3? Explain the angle relationship you used.



(b) What is the angle measurement of Angle 4? Explain the angle relationship you used.



(c) What is the angle relationship between angles 1, 2, & 3? What do you notice that is similar and different between the angle relationship between angles 1, 2, & 3 and that between 3 & 4?



(d) The combination of which two angles in the triangle equal angle 4? Use your work from Part C to figure out why this is the case, and explain your conclusion.


ANSWER ALL 4 PARTS FULLY AND EXPLANITORY!

Answer 1

Hmmm...

(a)

The angle measurement is

180-25-52=

180-77=

103 degrees

We calculated it this way because angle 3 was inside of a triangle, and we know that all the interior angles of a triangle would add up to 180. Two angles are already given as well, so we just need to subtract them to find out the angle of Angle 3

(b)

Angle 4 is just

180 minus Angle 3

which is

180-103=

77

I used supplementary angles

(meaning two angles add up to 180)

(c)

The angle relationship between Angles 1,2,and2 is supplementary angles because they all add up to 180 degrees. The angle relationship for Angles 3 and 4 are the same because they also add up to 180. I noticed that they are both supplementary, but one set of angles(3 and 4, specifically) only require two angles to become supplementary while the other set needs three(it's a triangle).

(d)

The combination of Angle 1 and 2 equals angle four. From question one, we derived that Angle 1 plus Angle 2 equals 77. From question two, we found out angle two equals 77. From part c, We procured that

Angle 1 + Angle 2 + Angle 3 = Angle 3 + Angle 4

Subtracting Angle 3 on both sides, we end up with:

Angle 1 + Angle 2=Angle 4

-Hunter