Question 45
The two remote interior angles 3x and 2x add to the exterior angle 150. This is an application of the remote interior angle theorem
2x+3x = 150
5x = 150
x = 150/5
x = 30
angle BAC = 2x = 2*30 = 60 degrees
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Question 46
Choice A is true because of what I mentioned in the previous problem.
Choice B is true because we can find that angle C is 180-150 = 30. Then we can say A+B+C = 2x+3x+30 = 180 as all three interior angles of any triangle always add to 180.
Choice C is true since the equation above x = 30 can be written as 3x-2x = 30. It's a bit of a strange thing to do this, but it's still a valid statement.
Choice D is not true since 2x+3x is 150, which isn't 180 or larger. Even if we didn't know about the 150 at all, we still can't have 2 interior angles of a triangle add to 180 or larger (refer back to choice B).
