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 DE side in one of the triangles?

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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