Answer:
Angle 1 = 75°
Angle 2 = 55°
Angle 3 = 55°
Angle 4 = 40°
Angle 5 = 140°
Angle 6 = 40°
Angle 7 = 75°
Angle 8 = 65°
Angle 9 = 115°
Step-by-step explanation:
1) We start with angle 2
Angle 2
Angles on a straight line = 180°
Hence,
b + 125° = 180°
b = 180° - 125°
b = 55°
Angle 2 = 55°
2)Angle 1
The sum of angles in a triangle = 180°
Hence
Let Angle 1 = a
50° + 55° + a = 180°
a = 180° - (50° + 55°)
a = 180° - 105°
a = 75°
3)Angle 3
Angle 2 and Angle 3 are vertical angles
So we use the Vertical angle theorem
This means
Angle 2 = Angle 3
Angle 2 = 55°
Hence, Angle 3 = 55°
4) Angle 4
Sum of Angles in a triangle = 180°
Let Angle 4 = d
Hence:
85° + Angle 3 + d = 180°
85° + 55° + d = 180°
d= 180° - (85° + 55°)
d = 180°- 140°
d = 40°
5)Angle 5
Angle 4 and Angle 5 are angles on a straight line
Sum of angles on a straight line = 180°
Angle 4 = 40°
Let Angle 5 = e
Hence:
40° + e = 180°
Collect like terms
e = 180° - 40°
e = 140°
6) Angle 6
Angle 4 and Angle 6 are vertical angles
Using Vertical angle theorem,
Angle 4 = Angle 6
Angle 4 = 40°
Hence, Angle 6 = 40°
7)Angle 9
Solving for Angle 9,
Sum of angles on a straight line = 180°
Angle 9 = i
i + 65° = 180°
i = 180° - 65°
i = 115°
8) Angle 8
= Angle 9 and Angle 8 are angles in a straight line
= Angle 8 = h
h + 115° = 180°
h = 180° - 115°
h = 65°
9)Angle 7
Sum of angles in a triangle = 180°
Angle 7 = g
g = 180° - (65° + Angle 6)
= 180° - (65 + 40
= 180° - 105°
= 75°
The rate of the kayak in still water is 3.5 mph
<h3><u>Solution:</u></h3>
Given that It takes 3 hours to paddle a kayak 12 miles downstream
Distance covered in downstream = 12 miles
Time taken to cover downstream = 3 hours
Also given that it takes 4 hours for the return trip upstream
Distance covered in upstream = 12 miles
Time taken to cover upstream = 4 hours
<em><u>Formula to remember:</u></em>
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then: Speed downstream = (u + v) km/hr and Speed upstream = (u - v) km/hr
Let the speed of Kayak in still water = x mph
And The speed of current = y mph
For downstream:
Speed downstream = x + y
We know that 
x + y = 4 ------ eqn 1
<em><u>For upstream:</u></em>
Speed upstream = x - y
x - y = 3 -------- eqn 2
Now let us eqn 1 and eqn 2
Add eqn 1 and eqn 2
x + y + x - y = 4 + 3
2x = 7
x = 3.5
speed of Kayak in still water = x mph = 3.5 mph
Answer:
Step-by-step explanation:
Its 43567 bc I searched it up
Answer:
Step-by-step explanation:
-3(y²+4y+4)-5+6y
=-3y²-12 y-12-5+6 y
=-3y²-6y-17
Answer:
D
Step-by-step explanation:
Because it is on the outside
