Calculate Angle FCD: Complex Geometry with 90°, 55°, and 95° Angles

It is known that angles A and D are equal to 90 degrees

Angle BCE is equal to 55 degrees

Angle DEB is equal to 95 degrees

Complete the value of angle FCD based on the data from the figure.

Let's break down angle FCD for an angle addition exercise:

$FCD=FCE+ECD$

Let's write down the known information from the question:

$FCD=30+ECD$

Since angle ECD is not given to us, we will calculate it in the following way:

Let's look at triangle EDC, where we have 2 angles.

Since we know that the sum of angles in a triangle equals 180 degrees, let's write down the data in the formula:

$ECD+CED+EDC=180$

$ECD+70+90=180$

Let's move terms and keep the appropriate sign:

$ECD=180-90-70$

$ECD=20$

Now we can substitute ECD in the formula we wrote earlier:

$FCD=30+ECD$

$FCD=30+20$

$FCD=50$