Question

100 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

#1

• <3 be x

Apply angle sum property

`\\ \rm\Rrightarrow x+25+52=180`

`\\ \rm\Rrightarrow x+77=180`

`\\ \rm\Rrightarrow x=103`

#2

Sum of two Interiors=exterior

• <4=25+52=77°

#3

Yes <1 ,<2,<3 have sum 180°.

#4

<2 and <1.

As sum of two Interiors=exterior