Sum and Difference of Angles: Calculate Angles in Quadrilaterals

Let's look at triangle CAD, the sum of angles in a triangle is 180 degrees, so we can find angle DAC:

$CAD+90+30=180$

$CAD+120=180$

$CAD=180-120$

$CAD=60$

Since ABCD is a rectangle, all angles are equal to 90 degrees.

Therefore angle CAB equals:

$90-CAD=90-60=30$

We know that CAD equals 30 degrees, since ABCD is a rectangle all angles are equal to 90 degrees.

CAB equals 60 degrees.

Therefore:

$CAD=BCA=30,ACD=CAB=60$

Note that the GDC angle is part of the EDC angle.

Therefore, we can write the following expression:

$GDC+EDG=EDC$

Since we know that angle D equals 90 degrees, we will substitute the values in the formula:

$GDC+40=90$

We will simplify the expression and keep the appropriate sign:

$GDC=90-40$

$GDC=50$

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:

$FCD=30+ECD$

$FCD=30+20$

$FCD=50$

Note that angle BAG is part of angle BAD.

Therefore, we can write the following equation:

$BAG+GAD=BAD$

From the data given in the question, we know that angle A is equal to 90 degrees, and angle GAD is equal to 50.

Let's substitute the known values into the formula:

$BAG+50=90$

We'll move terms to one side and maintain the appropriate sign:

$BAG=90-50$

$BAG=40$

Let's break down angle BCE into an angle addition exercise:

$BCE=BCF+FCE$

Now let's input the known data from the diagram:

$BCE=25+30$

$BCE=55$

Let's pay attention to the data in the question.

We know that angle DEB is equal to 95 degrees.

Let's break it down into an addition exercise:

$CEB+CED=DEB$

Now let's substitute the known data into the formula:

$CEB+70=95$

We'll move a term and keep the appropriate sign:

$CEB=95-70$

$CEB=25$

Let's look at angle BCD and break it down into the angles that compose it:

$BCD=BCF+FCE+ECD$

Note that the angle values we wrote in the formula are given to us in the diagram, and now we'll substitute them:

$BCD=25+30+20$

$BCD=75$