Answer:
70° is your measurement for ∠t.
Step-by-step explanation:
Note that a straight line has an angle of 180°
It is given to us that ∠r and ∠t = 180°, and that m∠r = 110°
Plug in 110 for ∠r
110 + ∠t = 180
Isolate ∠t. Note the equal sign, what you do to one side, you do to the other. Subtract 110 from both sides
110 (-110) + ∠t = 180 (-110)
∠t = 180 - 110
∠t = 70
70° is your measurement for ∠t.
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VK = VY+YK by the segment addition postulate. Basically adding two segments along a straight line forms a longer segment. In this case, VY and YK combine to form VK
Since VK = x and VY = 22, this means...
VK = VY+YK
x = 22+YK
x-22 = YK
YK = x-22
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Notice the arc marks where the point T is located. These markings tell us that the two angles VTY and YTK are congruent angles. Because of this, we can use the angle bisector theorem which says that the ratio of the corresponding sides are congruent.
In short, we can form this ratio
VT/VY = KT/KY
which is the ratio of the side adjacent to the angle, to the side opposite the angle
Plug in the given values and solve for x
VT/VY = KT/KY
77/22 = 87.5/(x-22)
77(x-22) = 22*87.5
77(x-22) = 1925
77x-77*22 = 1925
77x-1694 = 1925
77x = 1925+1694
77x = 3619
x = 3619/77
x = 47
Answer: 47
Answer:
2091
Step-by-step explanation:
We are given with three equations and three unknowns and we need to solve this problem. The solution is shown below:
Three equations are below:
3x + 4y - z = -6
5x + 8y + 2z = 2
-x + y + z = 0
use the first (multiply by +2) and use the second equation:
2 (3x+4y -z = -6) => 6x + 8y -2z = -12
+ ( 5x + 8y +2z = 2)
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11x + 16y = -10 -> this the fourth equation
use the first and third equation:
3x + 4y -z = -6
+ (-x + y + z =0)
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2x + 5y = -6 -> this is the fifth equaiton
use fourth (multiply by 2) and use fifth (multiply by -11) equations such as:
2 (11x + 16y = -10) => 22x + 32y = -20 -> this is the sixth equation
-11 (2x + 5y = -6) => -22x -55y = 46 -> this is the seventh equation
add 6th and 7th equation such as:
22x + 32y = -20
+(-22x - 55y = 66)
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- 23y = 46
<span> y = -2
solving for x, we have:
</span>2x + 5y = -6
2x = -6 - 5y
2x = -6 - (5*(-2))
2x = -6 +10
2x = 4
x=2
solving for y value, we have:
-x + y + z =0
z = x -y
z = 2- (-2)
z =4
The answers are the following:
x = 2
y = -2
z = 4
Answer:
m<2 = 73
Step-by-step explanation:
Since <1 and <2 are complementary (which means that they equal 90), all you have to do is subtract 17 from 90 to find your answer:
90 - 17 = 73
thus, m<2 = 73
