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

Angle Addition with Right Angle Decomposition

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.

505050404040707070AAABBBCCCDDDEEEFFFGGG3025

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

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 DEB is equal to 95 degrees

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

505050404040707070AAABBBCCCDDDEEEFFFGGG3025

2

Step-by-step solution

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

Therefore, we can write the following expression:

GDC+EDG=EDC GDC+EDG=EDC

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

GDC+40=90 GDC+40=90

We will simplify the expression and keep the appropriate sign:

GDC=9040 GDC=90-40

GDC=50 GDC=50

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Angle Addition: Adjacent angles combine to form larger angles
  • Technique: Use GDC + EDG = EDC, so GDC + 40° = 90°
  • Check: Verify 50° + 40° = 90° matches the right angle ✓

Common Mistakes

Avoid these frequent errors
  • Adding all visible angles instead of using angle relationships
    Don't add 50° + 40° + 70° thinking all angles must be used = 160° which exceeds a right angle! This ignores the geometric structure. Always identify which specific angles are adjacent and form the target angle.

Practice Quiz

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Find the measure of the angle \( \alpha \)

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FAQ

Everything you need to know about this question

How do I know which angles to add together?

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Look for angles that are adjacent (share a common ray) and together form the angle you're looking for. In this case, GDC and EDG are adjacent and together make angle EDC.

Why is angle D equal to 90 degrees?

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The problem states that angles A and D are both 90°. This means angle EDC (the full angle at point D) is a right angle, which we can use in our calculations.

What does it mean that GDC is 'part of' angle EDC?

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It means ray DG divides angle EDC into two smaller angles: EDG and GDC. These two parts add up to the whole angle EDC.

Can I solve this problem a different way?

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Yes! You could also think of it as: EDG + GDC = 90°, then substitute the known value of EDG (40°) to get the same answer.

How do I know if 50 degrees is reasonable?

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Check that it's less than 90° (since it's part of a right angle) and that when added to 40°, it gives exactly 90°. Both conditions are satisfied!

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