Compare Angles BAC and E: Analyzing 40° Geometric Relationships

Triangle Angle Comparison with Exterior Angles

Fill in the missing sign (?) according to the diagram:

Angle BAC ? angle E

404040404040AAABBBDDDEEECCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's complete the missing sign. Ready? Let's go!
00:10 Remember, a triangle's angles add up to 180 degrees. Subtract to find the missing angle. You got this!
00:17 This is the size of the angle you calculated. Nice work!
00:21 Looking at the drawing, angle E is obtuse, which means it's greater than 90 degrees. Good observation!
00:29 And that's the solution to our problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign (?) according to the diagram:

Angle BAC ? angle E

404040404040AAABBBDDDEEECCC

2

Step-by-step solution

Fist let's look at triangle ABC, remembering that the sum of angles in a triangle equals 180 degrees.

In triangle ABC, we are given two angles: 40 and 90.

Therefore, we can calculate BAC as follows:

BAC=1809040 BAC=180-90-40

BAC=50 BAC=50

Now let's look at angle E, noting that it is greater than 90 degrees.

Therefore:

E>BAC E > BAC

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Triangle Sum Rule: All interior angles in a triangle add to 180°
  • Calculation: BAC = 180° - 90° - 40° = 50°
  • Visual Check: Compare calculated 50° with larger exterior angle E ✓

Common Mistakes

Avoid these frequent errors
  • Comparing angles without calculating first
    Don't just look at the diagram and guess which angle is bigger = wrong comparisons! Visual estimation can be very misleading, especially with different angle types. Always calculate the unknown angle using the triangle sum rule before comparing.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

How do I know which angles are 40° in the triangle?

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Look at the angle markings in the diagram! The curved lines with "40" show you exactly which angles measure 40°. One is at vertex B and one is at vertex C.

Why is angle E greater than 90 degrees?

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Angle E appears to be an obtuse angle based on the diagram. It looks wider than a right angle (90°), making it larger than our calculated angle BAC of 50°.

What if I calculated BAC wrong?

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Double-check your arithmetic: 180°90°40°=50° 180° - 90° - 40° = 50° . Remember the right angle (square symbol) is 90°, not one of the 40° angles!

Can two different triangles have the same angle measures?

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Absolutely! Many triangles can share the same angle measures. What matters here is comparing the specific angles BAC and E from this particular diagram.

How do I remember the triangle sum rule?

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Think of it this way: if you walk around any triangle and return to your starting point, you've made exactly one complete turn = 360°. The interior angles are half of that!

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