we know that
m∠PTS=m∠RTQ -----> by vertical angles
Step 1
m∠RTQ+m∠QTS=
-------> by supplementary angles
solve for m∠QTS
m∠QTS=-m∠RTQ -------> equation 
Step 2
m∠PTS+m∠QTS= -------> by supplementary angles
solve for m∠QTS
m∠QTS=-m∠PTS -------> equation 
Step 3
equate equation and equation
-m∠RTQ=-m∠PTS
-m∠RTQ=-m∠PTS
so
m∠RTQ=m∠PTS
therefore
<u>the answer is the option A</u>
Sum of the measures of angles RTQ and QTS is 180°
Answer:
x=15, y=5
Step-by-step explanation:
x+y=20
x-y=10
Adding both equations;
(x+x) + (y-y) = 20+10
2x = 30
x = 30/2 = 15
Substitute x=15 into x+y=20
y= 20-x = 20-15= 5
Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
Answer:
3x²y+0.5y+1
Step-by-step explanation:
2+3x²y -0.5y+y -1
2 and -1 is 1
-0.5y and +y is +0.5y so the answer is...
34 / .40 = 85
I hope this helps :)
