Find Angle BCD: Complex Geometric Figure with 90° Perpendicular Angles

Question

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.

00:18 Let's find the angle, BCD.

00:21 Angle C, is the space between points B and D. Let's take a closer look!

00:28 Remember, the whole angle is just the sum of its smaller parts.

00:46 Now, we'll plug in the right numbers, based on what we have, and solve to find the angle!

01:08 And there you have it! That's how we solve the problem of finding angle BCD.

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:

$BCD=25+30+20$

$BCD=75$