In the given figure, find m∠RST, if m∠RSU = 43º and m∠UST = 23º.
1 answer:
Applying the angle addition postulate, the measure of angle RST is: 66°.
<h3>What is the Angle Addition Postulate?</h3>If two angles share a common vertex and a common side, they are adjacent angles that form a larger angle. According to the angle addition postulate, the sum of these two adjacent angles will give a sum that is equal to the measure of the larger angle they both form.
We know the following:
Measure of angle RSU = 43º
Measure of angle UST = 23º
In the diagram given, angle RSU and angle UST are adjacent angles that form a larger angle, angle RST.
Therefore, based on the angle addition postulate, the measure of angle RST = sum of the measures of angles RSU and UST.
Therefore, we would have:
m∠RST = m∠RSU + m∠UST
Substitute
m∠RST = 43 + 23
m∠RST = 66°
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Step-by-step explanation:
Hey there!
The midpoint formula is;
Where, (x1), (y1), (x2) and (y2) are the given coordinates.
<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
<h3>Answer: 154</h3>
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Explanation:
I'll be using the formula
which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.
While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".
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If you ride r = 15 coasters, then we have the following number of combinations
There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.
We'll use this result later, so let x = 136.
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If r = 16, then we follow the same steps as above. You should get 17C16 = 17
There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"
Let y = 17 so we can use it later
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Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.
Let z = 1
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Add up the values of x, y, and z to get the final answer
x+y+z = 136+17+1 = 154