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When a quadrilateral is inscribed in a circle, the opposite angles are supplementary.
x + 2 + 3x + 6 = 180
4x + 8 = 180
4x = 172
x = 43
Now solve for A
3(43) + 6 = A
129 + 6 = A
135 = A
The measure of angle A is 135 degrees.
Hope this helps =)
A. We are given that each person weighs 150 lb, each gear
per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.
Since each person only carries one gear, therefore total
weight per person in 160 lb (weight of person + weight of gear).
So let us say that x is the number of persons, the
inequality equation is:
160 x + 200 ≤ 1200
B. There are three groups that wish to rent the boat.
> Solve the inequality equation when x = 4
160 (4) + 200 ≤ 1200
840 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 5
160 (5) + 200 ≤ 1200
1000 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 8
160 (8) + 200 ≤ 1200
1480 ≤ 1200 (FALSE)
So only the 4 people group and 5 people group can safely
run the boat.
C. Find the maximum number of people that may safely use
the boat, solve for x:
160 x + 200 ≤ 1200
160 x ≤ 1000
x ≤ 6.25
Therefore the maximum number of people that can safely
use the boat is 6 people.