Find Angle BAD in Triangle: Given Angles 86°, 28°, and 122°

Triangle Angle Properties with Interior Line Segments

ABC is a triangle. What is the size of the angle BAD ∢\text{BAD} ?

AAABBBCCCDDD86x28122

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:05 The sum of angles in a triangle equals 180
00:10 Therefore angle DAC equals 180 minus the known angles
00:21 This is angle DAC
00:31 The total angle equals the sum of its parts
00:37 Let's isolate X
00:51 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

ABC is a triangle. What is the size of the angle BAD ∢\text{BAD} ?

AAABBBCCCDDD86x28122

2

Step-by-step solution

First, let's find the value of angle B.

Since the sum of angles in a triangle is equal to 180, the formula is:

1808628=66 180-86-28=66

Now let's look at angle ADB, we can calculate its value since we are given angle ADC.

180122=58 180-122=58

Now we can calculate angle BAD:

1806658=56 180-66-58=56

3

Final Answer

56

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: Interior angles always sum to exactly 180 degrees
  • Linear Pair: Adjacent angles on a straight line sum to 180° 180° (like 122°+58°=180° 122° + 58° = 180° )
  • Check: All angles in triangle BAD should add to 180° 180° : 56°+66°+58°=180° 56° + 66° + 58° = 180°

Common Mistakes

Avoid these frequent errors
  • Forgetting to find angle ADB before solving triangle BAD
    Don't use angle ADC (122°) directly in triangle BAD = wrong triangle! Angle ADC is outside triangle BAD and gives incorrect results. Always find the interior angle ADB first: 180° - 122° = 58°.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

Why can't I use angle ADC (122°) directly in triangle BAD?

+

Because angle ADC is outside triangle BAD! You need the interior angle ADB, which is 180°122°=58° 180° - 122° = 58° since angles on a straight line sum to 180°.

How do I know which triangle to focus on?

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Look for the triangle that contains the angle you're asked to find. Since we want angle BAD, we need triangle BAD, not triangle ABC.

What's the difference between angles ABC and ABD?

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Angle ABC is in the original triangle, while angle ABD is part of triangle BAD. They're the same angle in this problem since both refer to angle B in triangle ABC.

Why do we calculate 180 - 86 - 28 first?

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This finds angle B in triangle ABC. We need this angle because it's also angle ABD in triangle BAD, which helps us solve for angle BAD.

How can I double-check my answer?

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Add all three angles in triangle BAD: 56°+66°+58°=180° 56° + 66° + 58° = 180° . If they sum to exactly 180°, your answer is correct!

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