Solve for X: Finding Values in the Equation 90+X = 3X+60

Q: How do I know these two angles should be equal?

Look at the diagram! These angles appear to be corresponding angles formed by parallel lines and a transversal. Corresponding angles are always equal, so we can set $ 90 + X = 3X + 60 $.

Q: What if I move the X terms to the right side instead?

That works too! You'd get $ 90 - 60 = 3X - X $, which gives $ 30 = 2X $. Same answer, just a different path!

Q: Why can't I just guess and check the answer choices?

While you could try that, solving algebraically teaches you the method for any similar problem. Plus, it's faster and more reliable than testing each option!

Q: What do I do after finding X = 15?

Calculate the actual angle measures! $ 90 + 15 = 105° $ and $ 3(15) + 60 = 105° $. Both angles measure 105 degrees.

Q: Is there always exactly one solution to these equations?

For linear equations like this one, yes! You'll get exactly one value for X. Quadratic equations can have two solutions, but linear ones have just one.

Linear Equations with Angle Relationships

Calculate X and the value of the marked angles, if possible.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate X and the angles themselves

00:03 Vertical angles are equal to each other

00:06 Compare the expressions and solve for X

00:09 Arrange the equation

00:17 Isolate X

00:21 This is the value of X

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X and the value of the marked angles, if possible.

Step-by-step solution

To determine $X$ , we assume the angles are set equal based on the geometry suggested by parallel lines and a transversal:

Set $90 + X = 3X + 60$ , as these angles are likely equal considering the configuration.

Step-by-step solution:
1. Start by setting the equation: $90 + X = 3X + 60$ .
2. Simplify the equation by subtracting $X$ from both sides: $90 = 2X + 60$ .
3. Subtract $60$ from both sides: $30 = 2X$ .
4. Divide both sides by $2$ to solve for $X$ : $X = 15$ .

Therefore, the solution to the problem is $X = 15$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Equal Angles: Set expressions equal when angles have the same measure
Technique: Subtract X from both sides: 90 = 2X + 60
Check: Substitute X = 15: 90 + 15 = 105, 3(15) + 60 = 105 ✓

Common Mistakes

Avoid these frequent errors

Not recognizing when angles should be equal
Don't assume angles are different just because they have different expressions = missing the key relationship! The diagram shows these are corresponding angles or alternate interior angles. Always identify the geometric relationship first, then set up your equation.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

How do I know these two angles should be equal?

Look at the diagram! These angles appear to be corresponding angles formed by parallel lines and a transversal. Corresponding angles are always equal, so we can set $90 + X = 3X + 60$ .

What if I move the X terms to the right side instead?

That works too! You'd get $90 - 60 = 3X - X$ , which gives $30 = 2X$ . Same answer, just a different path!

Why can't I just guess and check the answer choices?

While you could try that, solving algebraically teaches you the method for any similar problem. Plus, it's faster and more reliable than testing each option!

What do I do after finding X = 15?

Calculate the actual angle measures! $90 + 15 = 105°$ and $3(15) + 60 = 105°$ . Both angles measure 105 degrees.

Is there always exactly one solution to these equations?

For linear equations like this one, yes! You'll get exactly one value for X. Quadratic equations can have two solutions, but linear ones have just one.

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