Answer:
x = 80 degrees
Explanation:
First look at the upper triangle. There are two 65 degree angles there, along with two equal sides. The angles must sum up to 180 degrees. Therefore:
2(65) + x = 180; thus, the value of x is 50 degrees.
Next, recognize that the vertical angles in the middle of the diagram are equal and are 50 degrees each. Thus, the smaller triangle has two 50-degree angles. Again we sum up the angles, obtaining 50 + 50 + x = 180, or x = 80 degrees