Solve for X: Triangle with 115° Angle and Expressions 8X and 20+X

Triangle Angle Sum with Algebraic Expressions

Calculate the value of X.

11511511520+X20+X20+XAAABBBCCC8X

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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
00:14 Collect like terms
00:18 Isolate X
00:28 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.

11511511520+X20+X20+XAAABBBCCC8X

2

Step-by-step solution

Let's remember that the sum of angles in a triangle is equal to 180.

Therefore, we will use the following formula:

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

We'll substitute the known data:

115+8x+20+x=180 115+8x+20+x=180

We'll combine similar terms:

9x+135=180 9x+135=180

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

9x=180135 9x=180-135

9x=45 9x=45

We'll divide both sides by 9:

x=5 x=5

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all three angles in any triangle equals 180°
  • Technique: Combine like terms: 8x and x become 9x in equation
  • Check: Substitute x = 5: 115° + 40° + 25° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms with different coefficients
    Don't leave 8x and x separate in your equation = wrong setup! This makes solving much harder and often leads to calculation errors. Always combine like terms: 8x + x = 9x before solving.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

Why does the sum of triangle angles always equal 180°?

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This is a fundamental geometric rule! No matter what shape or size triangle you have, the three interior angles will always add up to exactly 180°. It's like a mathematical law of triangles.

How do I combine 8x and x correctly?

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Think of it like this: 8x means 8 × x and x means 1 × x. So 8x + x = (8 + 1)x = 9x. Always add the coefficients (numbers in front) when combining like terms.

What if I get a decimal or fraction for x?

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That's completely normal! Not all triangle problems have whole number solutions. Just make sure your final angles still add up to exactly 180° when you substitute back.

Can I solve this without setting up an equation?

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No, you need the equation! Since you have unknown expressions (8x and 20+x), you must use the triangle angle sum rule: 115 + 8x + (20+x) = 180 to find x.

How do I know which angle has which expression?

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Look at the diagram carefully! The expressions 8x and 20+x are labeled next to their respective angles. The 115° is clearly marked at the top angle of the triangle.

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