Pick the best estimate for the measure of the angle. Option A) 195 degrees. Option B) 110 degrees. Option C) 255 degrees. Option D) 300 degrees. Option E) 150 degrees.
In a question like this, it’s important to note that we don’t actually measure the angle. What we need to do instead is to use what we know about angles in order to help us make a choice. So let’s start by reminding ourselves of some of the things we know about angles.
First, we have a right angle, 90 degrees, this sort of angle that you get at the corner of a room or the corner of a shape such as a square or a rectangle. Next, we have the angles on a straight line, 180 degrees and finally the angles about a point or in one complete rotation is 360 degrees. And when we’re talking about angles, we also use some different words to describe angles in a particular grouping.
An acute angle is one which is from zero degrees up to less than 90 degrees. An obtuse angle is greater than 90 degrees up to less than 180 degrees. Notice that we’ve missed out 90 degrees between acute and obtuse and that’s because a 90-degree angle is a right angle. And finally, a reflex angle is one that’s greater than 180 degrees.
So let’s have a look at our diagram then and see if we can add in any lines that might help us to estimate the size of it. And it’s important to note that when we’re looking at our diagram, we’re being asked to estimate the reflex angle 𝐴𝐵𝐶 and not the obtuse angle 𝐴𝐵𝐶. So if we continue our line 𝐴𝐵 to create a section 𝐴𝐵𝐷, this means that the angle of 𝐴𝐵𝐷 will be 180 degrees. We can also create a line 𝐵𝐸 coming down from point 𝐵, giving us a right angle or an angle of 90 degrees. So now, we can say that the angle is definitely greater than 180 degrees because it’s larger than a straight line. We can also say that if we were to look at the angle 𝐴𝐵𝐸 that this would be equal to 180 degrees plus 90 degrees, which is 270 degrees. And since our angle isn’t quite that big, then we know that our angle must be less than 270 degrees.
But let’s see if we can narrow down the range for the estimate of our angle. So since we know that the angle 𝐷𝐵𝐸 is a right angle, that means if we divide that angle in two, we will get 90 divided by two which is a 45-degree angle. So we could create an angle that’s equal to 180 degrees plus 45 degrees, so an angle of 225 degrees. But this angle isn’t as large as the angle that we’re asked to estimate. However, now, we can say that the angle must be between 225 degrees and 270 degrees.
And since there is only one of the given estimate options that fit, the answer must be 255 degrees.