Solve for X: Triangle Angles with Expressions 11X, 40X, and 80-X

Triangle Angle Sum with Variable Expressions

Calculate the value of X.

11X11X11X80-X80-X80-XAAABBBCCC40X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of X
00:03 The sum of angles in a triangle equals 180
00:07 Substitute in the relevant values according to the given data and proceed to solve for X
00:15 Take X out of the parentheses
00:22 Solve what's inside the parentheses
00:30 Isolate X
00:37 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the value of X.

11X11X11X80-X80-X80-XAAABBBCCC40X

2

Step-by-step solution

Let's remember that the sum of angles in a triangle equals 180 degrees.

Therefore, we will use the following formula:

A+B+C=180 A+B+C=180

Let's input the known data:

11x+40x+80x=180 11x+40x+80-x=180

We'll combine the x terms:

50x+80=180 50x+80=180

We'll move terms to one side and maintain the appropriate sign:

50x=18080 50x=180-80

50x=100 50x=100

We'll divide both sides by 50:

x=2 x=2

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: All angles in any triangle sum to 180 degrees
  • Technique: Combine like terms: 11x + 40x - x = 50x
  • Check: Verify angles: 22° + 80° + 78° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms correctly
    Don't add 11x + 40x + 80 - x = 131x + 80! This ignores the subtraction and gives x = 0.77 instead of 2. Always combine x terms carefully: 11x + 40x - x = 50x.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Why do triangle angles always add up to 180°?

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This is a fundamental property of triangles! No matter what size or shape the triangle is, the three interior angles will always sum to exactly 180 degrees.

How do I handle the negative x in (80-x)?

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Remember that 80 - x means you're subtracting x. When combining terms, write it as: 11x + 40x + (-x) = 50x. The negative sign stays with the x!

What if I get a negative value for x?

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Check your algebra! In this problem, x should be positive since all angle expressions (11x, 40x, 80-x) need to give positive angle measures.

Can I solve this differently?

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Yes! You could also substitute each angle expression directly: A+B+C=180° \angle A + \angle B + \angle C = 180° . But combining like terms first is usually faster.

How do I check if x = 2 is correct?

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Substitute back: 11(2)+40(2)+(802)=22+80+78=180° 11(2) + 40(2) + (80-2) = 22 + 80 + 78 = 180° ✓. Perfect!

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