Find x in Triangle ABC: Given Angles 111° and 60°

Triangle Angles with Exterior Angle Properties

Calculate the value of x x .

111°111°111°AAABBBCCC60°x

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Step-by-step video solution

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00:00 Find X
00:06 Supplementary angle to 180
00:16 Sum of angles in a triangle equals 180
00:25 Collect terms and isolate X
00:42 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Calculate the value of x x .

111°111°111°AAABBBCCC60°x

2

Step-by-step solution

Remember that a straight angle is equal to 180 degrees.

Therefore, we can work out that the angle measuring 111° and angle ACB form a straight angle.

Now let's calculate angle ACB as follows:

ACB=180111 ACB=180-111

ACB=69 ACB=69

Then we can calculate x x .

Remember that the sum of angles in a triangle is equal to 180 degrees, therefore:

X=1806960 X=180-69-60

X=51 X=51

3

Final Answer

51

Key Points to Remember

Essential concepts to master this topic
  • Linear Pairs: Adjacent angles on a straight line sum to 180°
  • Triangle Sum: Interior angles total 180°, so x=1806960=51° x = 180 - 69 - 60 = 51°
  • Check: Verify 51°+60°+69°=180° 51° + 60° + 69° = 180°

Common Mistakes

Avoid these frequent errors
  • Using exterior angle directly as interior angle
    Don't use the 111° angle as angle ACB in triangle calculations = wrong answer of 9°! The 111° is an exterior angle, not interior. Always find the interior angle first: 180° - 111° = 69°, then use triangle angle sum.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

What's the difference between interior and exterior angles?

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Interior angles are inside the triangle, while exterior angles are outside. The 111° shown is exterior - it's the angle formed by extending side AC beyond point C.

Why does the exterior angle equal 180° minus the interior angle?

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Because they form a linear pair - two adjacent angles on a straight line. Linear pairs always add up to 180°, so if one angle is 111°, the other must be 180° - 111° = 69°.

Can I solve this without finding the interior angle first?

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No! You must use the interior angles for triangle calculations. The exterior angle 111° can't be used directly in the triangle angle sum formula.

How do I identify which angles are interior vs exterior?

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Look at the triangle vertices. Interior angles are formed by two sides of the triangle meeting at a vertex. Exterior angles are formed when you extend one side beyond the vertex.

What if I get a negative angle?

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Check your work! Angles in triangles are always positive. A negative result usually means you used an exterior angle instead of the interior angle, or made an arithmetic error.

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