Sum and Difference of Angles: Calculate Angles in Quadrilaterals

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

Angle DEB is equal to 95 degrees

Angle BCE is equal to 55 degrees

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

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:

$BAG=90-50$

$BAG=40$

40

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

Angle DEB is equal to 95 degrees

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

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:

$GDC=90-40$

$GDC=50$

50

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

Angle FCD is equal to 50 degrees

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

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:

$CEB=95-70$

$CEB=25$

25

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

Angle FCD is equal to 50 degrees

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

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:

$BCD=25+30+20$

$BCD=75$

75

Angles A and D are both equal to 90 degrees.

Angle DEB is equal to 95 degrees.

Calculate the value of angle BCE based on the data in the figure.

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

$BCE=BCF+FCE$

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

$BCE=25+30$

$BCE=55$

55

The rectangle ABCD is shown below.

Angle CAD is equal to 45 degrees.

Calculate the remaining angles in the rectangle.

CAD = BCA = 30
ACD = CAB = 60

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.

50