Question

In the figure shown below, determine the value of x+y in degrees.

Answer 1

The sum of the interior angles of a triangle must be 180 degrees, so the angle C in the triangle ACE must be

$\begin{gathered} C=180-30-45 \\ C=105 \end{gathered}$

We see that the other angles that share the vertex with C are opposed by the vertex, so they must have the same measure, and, even more, they are supplementary with C, then these angles must be

$180-105=75$

75 degrees. Now, we can obtain x and y

$\begin{gathered} x=180-85-75=20 \\ y=180-75-75=30 \end{gathered}$

Then the sum is

$x+y=20+30=50$

So, the answer is (B) 50