Find X in the Angle Equation: (40+X)° and (120+X)° in Triangle Geometry

Q: How do I know these angles are supplementary?

Look at the diagram! The angles are adjacent (next to each other) and form a straight line. This geometric configuration always means the angles must add up to 180°.

Q: Why can't I just set the two angles equal to each other?

Setting them equal would mean $ 40 + X = 120 + X $, which gives 40 = 120 - impossible! The angles are different sizes but together they complete a straight line.

Q: What if I got X = 20 instead of X = 10?

Check your algebra! You might have forgotten to combine like terms properly. Remember: $ 40 + X + 120 + X = 160 + 2X $, not $ 160 + X $.

Q: How can I verify my answer is correct?

Substitute X = 10 back into both expressions: (40 + 10) = 50° and (120 + 10) = 130°. Then check: 50° + 130° = 180° ✓

Q: What does 'supplementary angles' mean exactly?

Supplementary angles are two angles that add up to exactly 180 degrees. When you see angles on a straight line, they're always supplementary!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate X

00:04 The adjacent angles form a straight angle (sum to 180)

00:07 Sum and equate to 180, solve for X

00:14 Collect like terms

00:22 Isolate X

00:42 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 X.

2

Step-by-step solution

To solve for $X$ , we must analyze the configuration formed by the angles $40 + X$ and $120 + X$ .

Step 1: Assume the angles are complementary based on the configuration, meaning they sum to 180 degrees.
Step 2: Formulate the equation based on this assumption: $(40 + X) + (120 + X) = 180$ .
Step 3: Simplify the equation: $40 + X + 120 + X = 180$ .
Step 4: Combine like terms to get $160 + 2X = 180$ .
Step 5: Solve for $X$ by subtracting 160 from both sides to yield $2X = 20$ .
Step 6: Divide by 2 to solve for $X$ , giving $X = 10$ .

Therefore, the value of $X$ is 10.

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic

Rule: Adjacent angles on a straight line sum to 180 degrees
Technique: Set up equation: (40 + X) + (120 + X) = 180
Check: Substitute X = 10: (50) + (130) = 180 ✓

Common Mistakes

Avoid these frequent errors

Assuming angles are equal instead of supplementary
Don't set (40 + X) = (120 + X) = this gives X = no solution! This ignores the straight line relationship. Always recognize that adjacent angles on a straight line must add to 180°.

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 adjacent (next to each other) and form a straight line. This geometric configuration always means the angles must add up to 180°.

Why can't I just set the two angles equal to each other?

+

Setting them equal would mean $40 + X = 120 + X$ , which gives 40 = 120 - impossible! The angles are different sizes but together they complete a straight line.

What if I got X = 20 instead of X = 10?

+

Check your algebra! You might have forgotten to combine like terms properly. Remember: $40 + X + 120 + X = 160 + 2X$ , not $160 + X$ .

How can I verify my answer is correct?

+

Substitute X = 10 back into both expressions: (40 + 10) = 50° and (120 + 10) = 130°. Then check: 50° + 130° = 180° ✓

What does 'supplementary angles' mean exactly?

+

Supplementary angles are two angles that add up to exactly 180 degrees. When you see angles on a straight line, they're always supplementary!

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