Answer:
9a) corresponding
9b) Congruent
9c) x=5
10) x=4
11=9
Step-by-step explanation:
9a. The angles are corresponding, as, if you look at the 8 angles as 2 groups of 4, they would be in the same spot.
b. Corresponding angles are congruent (by corresponding angles are congruent theorem)
c. Because the angles are congruent, we know that
23x-5=21x+5
23x-21x=5+5
2x=10
x=5
10. We know that (see attached photo) angle a is equal to angle b through the vertical angle theorem. Then, we know that angle b is equal to angle c through corresponding angles. So, we know that a=b, and b=c, so through the transitivity property, a=c, and c=90 degrees (it is a right angle)
Therefore, a=90 degrees
a=21x+6, so 21x+6=90
21x=84
x=4
11) This is almost the exact same problem as 10. We know that (see attached photo) a=b through vertical angles, and b=c through corresponding angles. Therefore, a=c
When you substitute the values of the two angles, we get:
-1+14x=12x+17
14x-12x=17+1
2x=18
x=9
