Select two answers from below. x=_ and then which theorem justifies your answer. (2x + 2)
(3x -63)
m
a
x=63
x=64
Ob
c
roob.
X=65
X=66
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Same Side Interior Angles
f

c. x=65

f. Alternate Exterior Angles

Step-by-step explanation:

2x+2=3x-63

2x=3x-65

-x=-65

x=65

They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4