Explanation for Question 20 From the Math (No Calc) Section on the Official Sat Practice Test 8
So number 20 gives us a circle with an angle in it X and 2 it tells us that the arc BC is two fifths of the circumference. 3 So this is two fifths or 40% of the circumference 4 of the circle. And they want to know what X is the angle. 5 And so what might be tripping you up with this question is that we 6 don't actually know the circumstances and we don't know what the radius is, 7 but that's not important for this one. What's important is this ratio the 40%, 8 if this arc is 40% of the total circumference, 9 then that means that this angle here X is 40% of 10 the total angle of the circle, right? 11 So the 40% arc is also meaning 40% angle. 12 And we know that the total angle of a circle is 360 degrees, 13 right? And so we can ask ourselves, 14 what is 40% of 360 degrees. 15 We can do that by multiplying by two over five. 16 If we do that, we can do 360 times two, 17 we get 0 12, 6, 7 27, 20 over 18 five. And then we can simplify that further by dividing by five 19 here. So five we'll go into seven. 20 Once that leaves us with two drop, 21 the two, five, we'll go into 20 to four times minus 20. 22 That'll leave us with, to drop the zero five goes into 24 times. 23 So that leaves us, leaves us with 144 degrees, 24 which is going to be our answer because 144 degrees is two fifths 25 of the total, um, angle of the circle just as 26 this arc was two fifths of the total circumference of the circle.