Question

PLEASE HELP!!!

Use this information for questions 9 to 11.
Question 9: What is ∠2? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.

Question 10: What is ∠4? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.

Question 11: With the given information and what you are able to determine, can you conclude that a ll b? If they are not parallel, explain why they are not. If they are parallel, what theorem can be used to prove them parallel? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.

Answer 1

Explanation:

p and q are parallel.

let's first only look at a and it's intersections with p and q.

based on the rules of intersecting lines (the angles of intersecting lines are the same in both sides of any of the lines, they are only left-right mirrored) and then parallel lines at that (the intersecting angles of a line with parallel lines are the same with every parallel line, otherwise they are not parallel).

angle 2 = angle 5 = angle 10 = angle 13

therefore,

8x + 14 = 10x - 10

14 = 2x - 10

24 = 2x

x = 24/2 = 12

angle 2 = 8×11 + 14 = 88 + 14 = 102°

because of the same rules of intersecting lines and parallel lines. it is also clear that

angle 4 = angle 7 = angle 12 = angle 15

therefore,

13y + 19 = 15y + 5

19 = 2y + 5

14 = 2y

y = 14/2 = 7

angle 4 = 13y + 19 = 13×7 + 19 = 91 + 19 = 110°

if a and b would be parallel too, then the principle of the same angles would be true not only top-down (as for the pervious 2 problems) but also left-right.

and then angle 2 would be equal to angle 4.

but they are not.

although the difference is small, it means a and b will intersect somewhere.

and they are therefore not parallel.