Solve for X: Triangle Angle Equation (120.2-X = 0.88X+50)

Q: Why do we set the sum equal to 180°?

This is the Triangle Angle Sum Theorem - one of the most important rules in geometry! The interior angles of any triangle always add up to exactly 180 degrees.

Q: How do I combine the x terms correctly?

Line up the coefficients: $ \frac{1}{2}x - 1x + 0.88x $. Convert to decimals: $ 0.5x - 1x + 0.88x = 0.38x $. Be careful with negative signs!

Q: What if I get a negative angle?

Check your work! Angles in a triangle must be positive. A negative result usually means an error in combining like terms or solving the equation.

Q: Can I solve this without converting fractions to decimals?

Yes! You can work with $ \frac{1}{2} $ throughout. Just be extra careful when combining $ \frac{1}{2}x - x + 0.88x $ to get $ \frac{38}{100}x $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 The sum of angles in a triangle equals 180

00:07 Substitute appropriate values according to the given data and solve for X

00:17 Take X out of the parentheses and collect terms

00:44 Solve what's inside the parentheses

00:52 Isolate X

01:07 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate the value of $x$ .

2

Step-by-step solution

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

Therefore, to find $x$ , we will use the following equation:

$A+B+C=180$

Now let's substitute in the known data:

$\frac{1}{2}x+6+120.2-x+0.88x+50=180$

We'll factor out $x$ as a common term in the equation:

$x(\frac{1}{2}-1+0.88)+176.2=180$

Let's next expand the parentheses:

$\frac{1}{2}x-x+0.88x+176.2=180$

Then, we'll combine the $x$ terms:

$0.38x+176.2=180$

Now we'll move terms to opposite sides and maintain the appropriate sign:

$\text{0}.38x=180-176.2$

$0.38x=3.8$

Finally, we will divide both sides by 0.38 to get our answer:

$x=10$

3

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Triangle Rule: Sum of all interior angles equals 180 degrees
Technique: Combine like terms: $\frac{1}{2}x - x + 0.88x = 0.38x$
Check: Verify angles add to 180°: 11° + 110.2° + 58.8° = 180° ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the third angle in the equation
Don't write 120.2-x + 0.88x+50 = 180 without the third angle = missing information! This ignores one of the triangle's angles and gives wrong results. Always identify all three angles and include them in your equation: angle A + angle B + angle C = 180°.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

Where does the third angle come from in this triangle?

+

Looking at the diagram, you can see three angles marked. The third angle at vertex A is $\frac{1}{2}x + 6$ . All three angles must be included in your equation.

Why do we set the sum equal to 180°?

+

This is the Triangle Angle Sum Theorem - one of the most important rules in geometry! The interior angles of any triangle always add up to exactly 180 degrees.

How do I combine the x terms correctly?

+

Line up the coefficients: $\frac{1}{2}x - 1x + 0.88x$ . Convert to decimals: $0.5x - 1x + 0.88x = 0.38x$ . Be careful with negative signs!

What if I get a negative angle?

+

Check your work! Angles in a triangle must be positive. A negative result usually means an error in combining like terms or solving the equation.

Can I solve this without converting fractions to decimals?

+

Yes! You can work with $\frac{1}{2}$ throughout. Just be extra careful when combining $\frac{1}{2}x - x + 0.88x$ to get $\frac{38}{100}x$ .

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Solve for X: Triangle Angle Equation (120.2-X = 0.88X+50)

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