If ray ST bisect <VSU, m<VST=6x+3 and m<TSU=3(x+12) calculate m<VSU
Assume T is on the interior of <VSU
Since ray ST bisects angle <VSU, we know that m<VST = m<TSU. Therefore, we can set 6x+3 equal to 3(x+12) and solve for x:
6x+3 = 3x+36
3x = 33
x = 11
Now that we have found x, we can plug it back into either equation to find m<VST or m<TSU:
m<VST = 6x+3 = 6(11)+3 = 69
m<TSU = 3(x+12) = 3(11+12) = 99
Since ray ST bisects angle <VSU, we know that m<VST + m<TSU = m<VSU. Therefore:
m<VSU = m<VST + m<TSU = 69 + 99 = 168
So, m<VSU is 168.
Answer Choices
69
21
138
42
The answer is 138.
We found that m<VST is 69 and m<TSU is 99. Since ST bisects angle <VSU, m<VST and m<TSU are equal, and their sum is twice the measure of angle STU. So,
2(m<VST) = 2(m<TSU) = m<VST + m<TSU = 69 + 99 = 168
Therefore, m<VSU = 168/2 = 84. Finally, since angle STU is a straight angle, we have:
m<VSU + m<STU = 180
Substituting 84 for m<VSU gives:
84 + m<STU = 180
m<STU = 180 - 84 = 96
Thus, we can check our answer:
m<VST = 69
m<TSU = 99
m<STU = 96
And we can verify that ST bisects angle <VSU.
a 3-d rectangle with points a-h what is the relationship that describes AB and FE
It is not clear what points in the 3-D rectangle correspond to A, B, F, and E. However, in any rectangle, the line segment connecting opposite vertices has a length equal to the square root of the sum of the squares of the lengths of the sides. In other words:
If ABCD is a rectangle, then AB = CD = sqrt(BC^2 + AD^2)
So, if we know the side lengths of the rectangular prism and the positions of the points A, B, F, and E, we can use the above formula to find the relationship that describes AB and FE. Without additional information about the rectangle, it is not possible to determine the relationship between AB and FE.
btw bot, in your first answer you have
m<TSU = 3(x+12) = 3(11+12) = 99
used to be 69 when I went to school