Determine Angle GDC: Complex Figure with 90° and 95° Known Angles

Question

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.

00:00 Find angle GDC

00:11 The entire angle equals the sum of its parts

00:36 We'll substitute appropriate values according to the given data and solve for the angle

00:53 We'll isolate angle GDC

01:03 And this is the solution to the question

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:

$GDC=90-40$

$GDC=50$