The diagram shows a protractor being used to measure the angle 𝜃. What is the value of 𝜃, in degrees?
Okay, so first things first, we can see on our diagram that we’ve got a protractor, the big blue semicircle. And with this protractor, we’re trying to measure the angle 𝜃. Now the angle 𝜃 is the angle between this line and this line or, in other words, this angle here.
Now before we make any measurements, we need to ensure that the protractor is lined up properly. So when we’re trying to measure the angle between two lines, the way to line up a protractor is that this plus symbol here should line up at the point where the two lines intersect.
So if we trace back the first line, it goes to the center of the plus sign. And if we line up the second line, it also goes towards the center of the plus sign. So the protractor is lined up properly. As well as this, we can see that this line over here is lined up with this line of the protractor, which could either be the 180-degree mark or the zero-degree mark.
Now because we’re going to be measuring the angle from here to here, we’re gonna be measuring counterclockwise. And therefore, we’re gonna say that this mark on the protractor represents the zero-degree mark. And hence, we’re going to be using the inner scale on the protractor, zero degrees, 10 degrees, 20 degrees, 30 degrees, and so on. We aren’t gonna use the outer scale which says 180 degrees, 170 degrees, and so on, because that’s for when we’re measuring clockwise.
So let’s say we had one line over here lined up with the zero mark and with the center of the plus sign. And we had another line going, let’s say for example, this way. Well then, we say that this line is at zero degrees. And the second line is at whatever this mark is here, in this case 115 degrees, because it’s between the 110-degree mark and the 120-degree mark.
However, we’re measuring counterclockwise. So this angle is going to end up being 10 degrees, 20 degrees, 30 degrees, and, under smaller graduations, 31, 32, 33 degrees, because each graduation represents one degree.
Now the way we know this is that between two large graduations, let’s say this one and this one, there’re nine different graduations. So if this line represents 50 degrees, then the smaller graduation represents 51, 52, 53, 54, 55, 56, 57, 58, 59. And this one is 60 degrees.
So anyway, we’ve just measured our angle 𝜃 to be 33 degrees. And so that is our final answer.