Answer: D) 116 degrees
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Step-by-step explanation:
The exterior angle shown is 4x. Right next to it, and inside the triangle, is the angle 180-4x. Note that 4x and 180-4x add to 180. These angles are supplementary.
The triangle has these three interior angles:
Those interior angles add up to 180 degrees. This is true of any triangle.
angle1+angle2+angle3 = 180
(63)+(x+24)+(180-4x) = 180
267-3x = 180
-3x = 180-267
-3x = -87
x = -87/(-3)
x = 29
This is not the final answer since we want the value of 4x. Be careful to avoid picking choice C. It's a trick answer.
If x = 29, then 4x = 4*29 = 116 is the final answer.
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Another approach:
We can use the remote interior angle theorem. This is the idea where adding any two interior angles gets us the exterior angle that isn't adjacent to either interior angle added. I recommend searching out "remote interior angle theorem" with quotes. Then look at the image search results to see visual examples of what's going on.
In this problem, we add up the 63 and (x+24) to get the 4x exterior angle.
63+(x+24) = 4x
x+87 = 4x
87 = 4x-x
87 = 3x
3x = 87
x = 87/3
x = 29
Then 4x = 4*29 = 116 points us to choice D as the final answer.