Calculate Angle BAC in a Right Triangle with 147° External Angle

External Angles with Right Triangle Properties

According to the data,

Calculate the size BAC ∢\text{BAC}

90°90°90°AAABBBCCC147°

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle A
00:04 Supplementary angle to a straight angle (180)
00:18 The sum of angles in a triangle equals 180
00:25 Let's collect terms and isolate BAC
00:48 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

According to the data,

Calculate the size BAC ∢\text{BAC}

90°90°90°AAABBBCCC147°

2

Step-by-step solution

Since we are given an angle of 147, let's calculate the angle ACB which complements it to 180 degrees:

180147=33 180-147=33

Now we have two angles in triangle ABC, and we can calculate angle BAC:

1809033=57 180-90-33=57

3

Final Answer

57

Key Points to Remember

Essential concepts to master this topic
  • External Angle Rule: External angle plus adjacent interior angle equals 180°
  • Technique: Find interior angle: 180° - 147° = 33°, then use triangle sum
  • Check: All angles sum to 180°: 57° + 90° + 33° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Using the external angle directly in triangle calculations
    Don't use 147° as an interior angle of the triangle = wrong sum over 180°! External angles are outside the triangle and must be converted first. Always subtract the external angle from 180° to find the interior angle.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

What exactly is an external angle?

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An external angle is formed when you extend one side of a triangle beyond a vertex. It's the angle outside the triangle, and it always adds up to 180° with its adjacent interior angle.

Why can't I just use 147° in my triangle calculation?

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Because 147° is outside the triangle! If you used it directly, your triangle's angles would add up to more than 180°, which is impossible. You must first find the interior angle.

How do I remember which angle is interior vs exterior?

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Look at the diagram carefully! The interior angle is inside the triangle shape, while the exterior angle is in the space outside the triangle where a side has been extended.

Is there a shortcut for this type of problem?

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Yes! Once you find the interior angle (180°147°=33°) (180° - 147° = 33°) , you can use: Missing angle = 180° - 90° - 33°. Just remember the triangle angle sum!

What if the triangle wasn't a right triangle?

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The same method works! Find the interior angle from the external angle, then use the fact that all triangle angles sum to 180° regardless of the triangle type.

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