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

Q: How do I know which angles to add together?

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.

Q: Why is angle D equal to 90 degrees?

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.

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

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

Q: Can I solve this problem a different way?

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

Q: How do I know if 50 degrees is reasonable?

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!

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.

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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

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.

Step-by-step solution

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

Therefore, we can write the following expression:

$GDC+EDG=EDC$

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:

$GDC=90-40$

$GDC=50$

Final Answer

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

Test your knowledge with interactive questions

a is parallel to b.

Calculate the angles shown in the diagram.

FAQ

Everything you need to know about this question

How do I know which angles to add together?

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?

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?

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?

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?

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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