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
Answer:
x = 96
