All drawings in the math section are drawn to scale. *Unless they specifically say they are not, as in “NOTE: Figures not drawn to scale.”
Use your eyes
So, use the fact that they are drawn to scale to your advantage. Here is question 9 from Test 5, Section 2 in the Blue Book.
Clearly, x is greater than 90 degrees. (You can draw a line perpendicular to line m just to check) And it looks like it is probably greater than 100 or 110 degrees as well. So cross out choices D and E.
Eyeballing it, it looks like line k is a little more than halfway between my red line and line m. So angle x is going to be greater than 90+45=135 degrees. Cross out choice C. (Notice that you are now in a good guessing position, btw.)
Use your “ruler”
How can I figure out whether angle x is 140 or 150 degrees? Hmm… what about using your “ruler” (otherwise known as the edge of your paper)?
Mark the 50 degree angle on your paper. Line it up to add to your 90 degree angle. Still short. So angle x is larger than 90+50 = 140. Cross out answer B. Choice A must be the right answer. (It’s usually faster just to solve the problem mathematically or algebraically or geometry-ically (which really should be a word.)
To solve this one more quickly, you could recognize that the angle next to (supplementary to) the 80 degree angle is 100 degrees. Which means that the third angle in that triangle must be 30 degrees. Using the rule of corresponding angles with parallel lines, the angle next to x must also be 30 degrees. Which means angle x must be 150 degrees.)
Use your brain
But what about when pictures ARE NOT drawn to scale? This is question 15 from Test 5, Section 2 in the Blue Book.
See how it says that the figures are NOT drawn to scale? Then we can’t rely on our eyeballs whatsoever. I know that they LOOK like they are the same size. But 0 isn’t the right answer for two reasons: 1. The figures aren’t drawn to scale. 2. This is a medium difficulty problem (given that it is question 15 in the section.) Medium level questions DO NOT have easy answers. Here’s the solution to this one (no eyeballing involved!)
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