Question

What is the value of x?

Answer 1

Answer:

x = 80 degrees

Step-by-step 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