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Remote Interior Angles - Problem 3
Recall that by the triangle angle sum theorem that the sum of the angles within a triangle is 180°. So, if the interior angles are given in terms of x, add the expressions together. Solve for x using techniques from algebra. Plug the value of x into the remote interior angles to find their measures. The measure of the exterior angle is the sum of these remote interior angles.
As always we can take algebra and apply to geometry. So here I’m asking you to find y. We are going to have to do this in two steps.
The first is, what is x? Well we know that 2x, 5x and 3x have to add up to be 180. So if I do that in my head, 2 and 5 is 7, 7 and 3 is 10. So 10x equals 180 degrees. If I divide by 10 I see that x must be 18 degrees.
So you have a choice here. You can substitute in here and then do a linear pair, but since we’re talking about remote exterior angles and remote interior angles, I’m going to say that 2x and 5x, which is 7x, has to equal y.
So if I substitute in 18 for x, we have 7 times 18 equals y, so 7 times 18 is 126 degrees.