Explanation for Question 11 From the Math (No Calc) Section on the 2019 October Sat
So 11 tells us in the X, Y plane points, 2 P Q and R lie on a circle with the center of O and 3 the degree measures of P O Q. 4 So that is going to be right here. P O Q is 30 degrees 5 and R O T right here is also 30 degrees. 6 And then they want to know what is the angle measure in radians of 7 angled, Q O R and Q O R is right here. 8 So this is what we're looking at. And so the best way to go 9 about this question is first to find the angle measure in the ind degrees 10 and then convert the degrees into radians. 11 We can find the ankle measure in degrees by not focusing on the circle 12 here, but rather focusing on how this right here is a straight line. 13 And my two, two of my angles on the straight line are a 30 14 and a 30. 15 And then I have the one that I'm looking for, which I'll call X. 16 And we should know that all of the angles on a straight line when 17 added together equal 180 degrees. 18 So if I do 30 plus 30 plus X, 19 that gives me a total angle measure of 180 degrees. 20 We can now see that 30 plus 30 is 60 and simplify this equation 21 to be 60 plus X is equal to 180, 22 and then to solve for X, I simply need to subtract 60 from both 23 sides. That way these sixties will cancel and I'll be left 24 with X is equal to 120. 25 Now that 120 is in degrees, 26 right? And I need to now convert degrees to radians. 27 And the conversion factor of degrees to radians will always be 180 degrees 28 is equal to PI radiance, 29 right? And so we can think about doing thi...