Given:
Tangent segment MN = 6
External segment NQ = 4
Secant segment NP =x + 4
To find:
The length of line segment PQ.
Solution:
Property of tangent and secant segment:
If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the product of the tangent segment.



Subtract 16 from both sides.


Divide by 4 on both sides.


The length of line segment PQ is 5 units.
1st part: you do 180 - 110 = 70
Why you subtract 180 from 110 is linear adds up to 180, so 70 + 110 would get 180 if that makes sense.
2nd part: 180 - 115 = 65
This is similar concept to what I explained with the first part.
3rd part: Triangle sum theorem is 180
4th part: To get angle 7 I believe you just subtract
180 - 70 - 65 = 45
5th part: 7 and 6 I believe are vertical angles and vertical angles are congruent which would make 6 = 7
6 would also = 45
Although I cannot see the options for each of the question(s) choices, I hope this can help you. :)
First combine like terms
you get
2d- 2e
hope this helps