Find X in Circle Sectors: Solving 3x+4 and 5x+16 Angle Relationship

Q: How do I know these angles are supplementary?

Look at the diagram! The angles are positioned on a straight line, which means they form a linear pair. Linear pairs are always supplementary, so they must add up to $ 180° $.

Q: What if I set the angles equal to each other instead?

That would only work if the angles were vertical angles or marked as equal. Since these angles are on a straight line, they're supplementary, not equal. Always identify the angle relationship first!

Q: Why do we get 8x + 20 = 180?

When you expand $ (3x+4) + (5x+16) = 180 $, you combine like terms: Combine x terms: $ 3x + 5x = 8x $Combine constants: $ 4 + 16 = 20 $

Q: How can I check if x = 20 is correct?

Substitute back into both original expressions: $ 3(20) + 4 = 60 + 4 = 64° $$ 5(20) + 16 = 100 + 16 = 116° $Check: $ 64° + 116° = 180° $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's find the value of X.

00:15 Remember, angles that are next to each other add up to one hundred eighty degrees.

00:21 Now, let's gather similar terms together.

00:28 Next, we need to get X by itself on one side of the equation.

00:46 And there you have it! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Find the value of the parameter x.

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Apply the triangle angle sum property.
Step 2: Combine like terms in the equation.
Step 3: Solve the resulting linear equation for $x$ .

Now, let's work through each step:
Step 1: Based on our assumption, the angles $3x + 4$ and $5x + 16$ should sum to 180 degrees. We write the equation:
$(3x + 4) + (5x + 16) = 180$ .

Step 2: Combine like terms:
$3x + 5x + 4 + 16 = 180$ .

Step 3: Simplify the equation:
$8x + 20 = 180$ .

Subtract 20 from both sides:
$8x = 160$ .

Finally, divide by 8 to solve for $x$ :
$x = \frac{160}{8} = 20$ .

Therefore, the solution to the problem is $x = 20$ .

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic

Supplementary Angles: Two angles that sum to exactly 180 degrees
Technique: Set up equation (3x+4) + (5x+16) = 180
Check: Substitute x=20: (60+4) + (100+16) = 64+116 = 180 ✓

Common Mistakes

Avoid these frequent errors

Assuming angles are vertical or equal
Don't set 3x+4 = 5x+16 just because angles look similar = wrong relationship! This ignores that these are supplementary angles forming a straight line. Always check if angles add to 180° when they form a linear pair.

Practice Quiz

Test your knowledge with interactive questions

It is possible for two adjacent angles to be right angles.

FAQ

Everything you need to know about this question

How do I know these angles are supplementary?

+

Look at the diagram! The angles are positioned on a straight line, which means they form a linear pair. Linear pairs are always supplementary, so they must add up to $180°$ .

What if I set the angles equal to each other instead?

+

That would only work if the angles were vertical angles or marked as equal. Since these angles are on a straight line, they're supplementary, not equal. Always identify the angle relationship first!

Why do we get 8x + 20 = 180?

+

When you expand $(3x+4) + (5x+16) = 180$ , you combine like terms:

Combine x terms: $3x + 5x = 8x$
Combine constants: $4 + 16 = 20$

How can I check if x = 20 is correct?

+

Substitute back into both original expressions:

$3(20) + 4 = 60 + 4 = 64°$
$5(20) + 16 = 100 + 16 = 116°$
Check: $64° + 116° = 180°$ ✓

What if my answer doesn't make the angles add to 180°?

+

Go back and check your algebra! Common errors include:

Wrong signs when combining terms
Calculation mistakes when solving
Setting up the wrong equation initially

The final check should always give you 180°.

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Find X in Circle Sectors: Solving 3x+4 and 5x+16 Angle Relationship

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