Find Angle BAG: Complex Geometry with 90°, 95°, and 55° Angles

Q: Why does angle A equal exactly 90 degrees?

The problem states that angles A and D equal 90 degrees. This tells us we're working with a rectangle where all corner angles are right angles!

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

Look at the diagram carefully! Angle BAG and angle GAD are adjacent angles that together make up the complete angle BAD (which is angle A = 90°).

Q: Can I use the other given angles like 95° and 55°?

Those angles (DEB = 95° and BCE = 55°) are not needed for finding angle BAG. Focus only on the angles that make up angle A: BAG + GAD = 90°.

Q: How do I check my answer is correct?

Add your answer to the given angle: $ 40° + 50° = 90° $. Since this equals angle A, your answer is correct!

Angle Decomposition with Rectangle Properties

Angles A and D equals 90 degrees.

Angle DEB equals 95 degrees.

Angle BCE equals 55 degrees.

Calculate angle BAG based on the data in the figure.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find angle BAG

00:09 Angle A between points B and G

00:15 The entire angle equals the sum of its parts

00:35 Let's substitute the angle values and solve for angle BAG

00:51 Let's isolate angle BAG

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

Angles A and D equals 90 degrees.

Angle DEB equals 95 degrees.

Angle BCE equals 55 degrees.

Calculate angle BAG based on the data in the figure.

Step-by-step solution

Note that angle BAG is part of angle BAD.

Therefore, we can write the following equation:

$BAG+GAD=BAD$

From the data provided in the question, we know that angle A is equal to 90 degrees and angle GAD is equal to 50 degrees.

Let's now substitute the known values into the formula:

$BAG+50=90$

We'll then move like terms to one side, maintaining the appropriate sign:

$BAG=90-50$

$BAG=40$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: All corner angles equal 90 degrees exactly
Technique: Use angle addition: BAG + GAD = BAD = 90°
Check: Verify 40° + 50° = 90° matches given angle A ✓

Common Mistakes

Avoid these frequent errors

Ignoring that angle A is a right angle
Don't try to find BAG without using the fact that angle A = 90°! This leads to guessing or using irrelevant angle measures from the diagram. Always identify that BAG + GAD must equal the total angle A = 90°.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

Why does angle A equal exactly 90 degrees?

The problem states that angles A and D equal 90 degrees. This tells us we're working with a rectangle where all corner angles are right angles!

How do I know which angles to add together?

Look at the diagram carefully! Angle BAG and angle GAD are adjacent angles that together make up the complete angle BAD (which is angle A = 90°).

What if I can't see the 50° angle clearly in the diagram?

The problem gives you all necessary information in text form. Look for angle GAD = 50° marked in the diagram, but rely on the written problem statement for exact values.

Can I use the other given angles like 95° and 55°?

Those angles (DEB = 95° and BCE = 55°) are not needed for finding angle BAG. Focus only on the angles that make up angle A: BAG + GAD = 90°.

How do I check my answer is correct?

Add your answer to the given angle: $40° + 50° = 90°$ . Since this equals angle A, your answer is correct!

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