Solve for X: Circle Angles with Expressions 2X-20 and 2X+20

Q: How do I know these angles are on a straight line?

Look at the diagram carefully! The angles are adjacent (next to each other) and together they form a straight line. This means they are supplementary angles that must add up to $ 180^\circ $.

Q: Why do the +20 and -20 cancel out?

When you add $ (2X - 20) + (2X + 20) $, the -20 and +20 are opposites that cancel each other out, leaving you with $ 2X + 2X = 4X $.

Q: What if I get a negative angle?

Angles in geometry problems are typically positive. If you get a negative result, check your setup - you might have the wrong relationship between the angles or made an algebra error.

Q: How do I check if X = 45 is really correct?

Substitute back: $ 2(45) - 20 = 70^\circ $ and $ 2(45) + 20 = 110^\circ $. Then verify: $ 70^\circ + 110^\circ = 180^\circ $ ✓

Step-by-step video solution

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Step-by-step written solution

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1

Understand the problem

Calculate X.

2

Step-by-step solution

To solve this problem, we will use the fact that the sum of angles on a straight line is $180^\circ$ . The angles given are $2X - 20$ and $2X + 20$ .

Step 1: Set up the equation for the sum of angles: $(2X - 20) + (2X + 20) = 180$ .
Step 2: Simplify the equation:

The equation simplifies as:

(2X - 20) + (2X + 20) = 4X

Step 3: Set $(4X = 180)$ .
Step 4: Solve for $X$ . Divide both sides of the equation by 4:

$4X = 180$

Thus,

X = \frac{180}{4} = 45

Therefore, the value of $X$ is $45$ .

3

Final Answer

45

Key Points to Remember

Essential concepts to master this topic

Angle Rule: Adjacent angles on a straight line sum to $180^\circ$
Technique: Combine like terms: $(2X - 20) + (2X + 20) = 4X$
Check: Verify $2(45) - 20 + 2(45) + 20 = 90 + 110 = 180^\circ$ ✓

Common Mistakes

Avoid these frequent errors

Not recognizing that angles on a straight line sum to 180°
Don't assume the angles are equal or add up to 90° = wrong equation setup! This leads to incorrect values like X = 25 or X = 10. Always identify the geometric relationship first - adjacent angles on a straight line must sum to 180°.

Practice Quiz

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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 angles are on a straight line?

+

Look at the diagram carefully! The angles are adjacent (next to each other) and together they form a straight line. This means they are supplementary angles that must add up to $180^\circ$ .

Why do the +20 and -20 cancel out?

+

When you add $(2X - 20) + (2X + 20)$ , the -20 and +20 are opposites that cancel each other out, leaving you with $2X + 2X = 4X$ .

What if I get a negative angle?

+

Angles in geometry problems are typically positive. If you get a negative result, check your setup - you might have the wrong relationship between the angles or made an algebra error.

Can I solve this without setting up an equation?

+

No! Since both angles contain the variable X, you need algebra to find the value. The key insight is recognizing that supplementary angles sum to 180°.

How do I check if X = 45 is really correct?

+

Substitute back: $2(45) - 20 = 70^\circ$ and $2(45) + 20 = 110^\circ$ . Then verify: $70^\circ + 110^\circ = 180^\circ$ ✓

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