Triangle Angle Calculation: Find X and Y Given 43° and 47° Angles

First, let's note that in triangle ACB we are given two angles.

Angle ABC equals 47 degrees, angle ACB equals 90 degrees.

Since the sum of angles in a triangle equals 180, we can calculate angle BAC and find the value of Y as follows:

$180-90-47=43$

Now let's look at triangle ACD, where we are also given two angles.

Angle CAD equals 43 degrees, angle ACD equals 90 degrees.

Since the sum of angles in a triangle equals 180, we can calculate angle ADC and find the value of X as follows:

$180-90-43=47$