Answer: x = 142
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Step-by-step explanation:
Method 1
Let y be the interior angle next to angle x.
Those angles are supplementary. This means x+y = 180
Furthermore, the interior angles of the triangle add to 180. This is true of any triangle.
y+34+108 = 180
y+142 = 180
y = 180-142
y = 38
Then,
x+y = 180
x = 180-y
x = 180-38
x = 142
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Method 2
Use the remote interior angle theorem. It says that adding any two interior angles will result in the exterior angle not adjacent to the interior angles. Search out "remote interior angle theorem" with quotes, and look at the image search results to see examples of what I mean.
The remote interior angles 34 and 108 add up to exterior angle x. This exterior angle is not adjacent to the interior angles mentioned.
We can simply say:
x = 34+108 = 142