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

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:

$FCD=30+ECD$

$FCD=30+20$

$FCD=50$