The first thing we do in a problem like this is let arc AB equal X. X is the magic letter, anything you need to find name it x. We also know that all arcs in a circle must add up to 360, so arc ALB is equal to 360 - x.
There's this theorem saying that when two tangents intersect from a point outside a triangle, the measure of the angle formed by the intersection of the tangents (angle P) is equal to the half the difference of the arcs.
This basically means:
angle P = 1/2(360 - x) - x.
plug in the value of angle P
84 = 1/2(360 - x - x)
168=360 - 2x
2x = 192
x = 96
arc AB=96
Answer:
The minimum number of full hours did Carson need to work at his father's business is 8 hours and 15 minutes
Step-by-step explanation:
Given as :
The total number of hours did Carson spent as baby sitting on one week = 5 hours
The rate at which he earn for baby sitting = $6 per hours
The rate at which he earn as job = $8 per hours
The total amount he will earn that week = $96
Let The minimum number of full hour he need to work = h
Now, According to question
The total amount he will earn that week = total number of hours did Carson spent as baby sitting on one week ×The rate at which he earn for baby sitting + The rate at which he earn as job × The minimum number of full hour he need to work
I.e $96 = $6 × 5 + $8 × h
Or, $96 = $30 + $8 × h
Or, 8 × h = 96 - 30
Or, 8 × h = 66
∴ h =
i.e h = 8.25 hours
So, The number of hours = h = 8 hours and 15 minutes
Hence,The minimum number of full hours did Carson need to work at his father's business is 8 hours and 15 minutes .
1/2x(6x9x1)+15
1/2x(6x9)+15
1/2x54+15
27+15
42