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:
Mean: 40.17 years.
Standard deviation: 10.97 years.
Step-by-step explanation:
The frequency distribution is in the attached image.
We can calculate the mean adding the multiplication of midpoints of each class and frequency, and dividing by the sample size.
The midpoints of a class is calculated as the average of the bounds of the class.
Then, the mean can be written as:
The standard deviation can be calculated as:
![s=\sqrt{\dfrac{1}{N-1}\sum f_i(X_i-E(X))^2}\\\\\\s=\sqrt{\dfrac{1}{59}[3(15-40.17)^2+7(25-40.17)^2+18(35-40.17)^2+20(45-40.17)^2+12(55-40.17)^2]}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cdfrac%7B1%7D%7BN-1%7D%5Csum%20f_i%28X_i-E%28X%29%29%5E2%7D%5C%5C%5C%5C%5C%5Cs%3D%5Csqrt%7B%5Cdfrac%7B1%7D%7B59%7D%5B3%2815-40.17%29%5E2%2B7%2825-40.17%29%5E2%2B18%2835-40.17%29%5E2%2B20%2845-40.17%29%5E2%2B12%2855-40.17%29%5E2%5D%7D)
In math remaining means left over.
Hope that helped:)
This image shows that these triangles are not congruent because they don’t line up
