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

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.

404040505050404040505050707070252525AAABBBCCCDDDEEEFFFGGG203025

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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.

404040505050404040505050707070252525AAABBBCCCDDDEEEFFFGGG203025

2

Step-by-step solution

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

BCD=BCF+FCE+ECD 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=25+30+20

BCD=75 BCD=75

3

Final Answer

75

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations