Find Angle Alpha: Solving 2x+30 and x+30 in Intersecting Lines

Q: Why do I need to set the angles equal to 180°?

Because the angles are supplementary - they form a straight line! When two angles share a straight line, they must add up to exactly 180°.

Q: How do I know which expressions go with which angles?

Look at the diagram carefully! The angle labeled $ 2x + 30 $ and the angle labeled $ \alpha = x + 30 $ are positioned as supplementary angles on the same line.

Q: What if I get a negative value for x?

Check your algebra! In this problem, x should be positive since we're dealing with angle measures. A negative x often means an error in combining like terms or solving the equation.

Q: Do I substitute x back into both expressions?

You only need to substitute into $ \alpha = x + 30 $ to find the answer. But it's good practice to check that both angles add to 180° as verification!

Q: Why isn't α just equal to 2x + 30?

The problem tells us that $ \alpha = x + 30 $, which is different from $ 2x + 30 $. These are two separate angles that happen to be supplementary.

Supplementary Angles with Algebraic Expressions

Find the size of the angle $\alpha$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the size of angle A

00:03 The entire angle equals the sum of its parts

00:09 A straight angle equals 180

00:13 Substitute in the value of A according to the given data and proceed to solve for X

00:22 Group terms

00:32 Isolate X

00:45 This is the size of X

00:48 Substitute in the value of X and proceed to solve for A

00:57 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the size of the angle $\alpha$ .

Step-by-step solution

To find the size of angle $\alpha$ , we proceed as follows:

Step 1: Establish the relationship for the angles as supplementary: $\alpha + (2x + 30) = 180^\circ$ .
Step 2: Substitute $\alpha = x + 30$ into the equation:

Substituting, we get:

(x + 30) + (2x + 30) = 180

Combine like terms:

3x + 60 = 180

Step 3: Solve for $x$ :
Subtract 60 from both sides:

3x = 120

Divide both sides by 3:

x = 40

Step 4: Substitute $x = 40$ back into $\alpha = x + 30$ to find $\alpha$ :

$\alpha = 40 + 30 = 70$

Thus, the size of the angle $\alpha$ is 70.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Supplementary angles on a straight line always sum to 180°
Technique: Substitute α = x + 30 into (2x + 30) + α = 180°
Check: Verify 70° + 110° = 180° when x = 40 ✓

Common Mistakes

Avoid these frequent errors

Setting angles equal instead of finding their sum
Don't write (2x + 30) = (x + 30) = 180°! This incorrectly treats each angle as 180°, not their combined total. Always add the supplementary angles together to equal 180°.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Why do I need to set the angles equal to 180°?

Because the angles are supplementary - they form a straight line! When two angles share a straight line, they must add up to exactly 180°.

How do I know which expressions go with which angles?

Look at the diagram carefully! The angle labeled $2x + 30$ and the angle labeled $\alpha = x + 30$ are positioned as supplementary angles on the same line.

What if I get a negative value for x?

Check your algebra! In this problem, x should be positive since we're dealing with angle measures. A negative x often means an error in combining like terms or solving the equation.

Do I substitute x back into both expressions?

You only need to substitute into $\alpha = x + 30$ to find the answer. But it's good practice to check that both angles add to 180° as verification!

Why isn't α just equal to 2x + 30?

The problem tells us that $\alpha = x + 30$ , which is different from $2x + 30$ . These are two separate angles that happen to be supplementary.

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