Triangle angle theorems
the value of x is

To find the value of x, you can calculate two interior angles using the given angles measures, and then find the third interior angle measure.

First off, the angles measuring 134° and 130° are supplementary with their adjacent interior angles. Supplementary angles add to equal 180 degrees, so solving the following equations for x will render two interior angles of the triangle.

180 = 134 + x
46 = x

180 = 130 + x
50 = x 

Now that we have two interior angles, we can find the third and use the rule applied above to find the measure of x in the diagram. The sum of the interior angles measures of all triangles is 180 degrees, so...

180 = 50 + 46 + x
180 = 96 = x
84 = x

The interior angle adjacent to the x in the diagram measures 84 degrees. As stated, these angles are supplementary, so the same set up can be used to solve for x - the x you need as an answer.

180 = 84 + x
96 = x

x = 96