Triangle Angle Calculation: Finding Angle A When B=2A and C=3B

Q: Why do I need to express everything in terms of angle A?

You need one variable to solve the equation! Since B = 2A and C = 3B = 6A, expressing everything as multiples of A gives you one equation with one unknown.

Q: How do I know that C = 6A and not just 3B?

Since B = 2A, you substitute: C = 3B = 3(2A) = 6A. This is substitution - replacing B with its equivalent expression in terms of A.

Q: What if my angle calculations don't add up to 180°?

Check your substitutions! Make sure you correctly wrote $ C = 3B = 3(2A) = 6A $, then verify $ A + 2A + 6A = 9A = 180° $.

Q: Can triangles have angle relationships like this in real life?

Absolutely! Many triangles have angles in specific ratios. For example, in a 1:2:6 ratio triangle like this problem, you get a very sharp triangle with angles 20°, 40°, and 120°.

Q: Is there a faster way to solve this without algebra?

The algebraic method is actually the fastest way! You could guess and check, but setting up $ A + 2A + 6A = 180° $ gives you the answer in just two steps.

Triangle Angles with Algebraic Relationships

$∢B$ is 2 times bigger than $∢A$ and $∢C$ is 3 times bigger than $∢B$ .

Calculate $∢A$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate angle A

00:05 The sum of angles in a triangle equals 180

00:11 Let's substitute appropriate values according to the given data and solve for angle B

00:21 Let's group terms

00:31 Let's isolate angle B

00:41 This is angle B

00:47 Let's substitute this value in the expression for angle A to find angle A

00:55 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$∢B$ is 2 times bigger than $∢A$ and $∢C$ is 3 times bigger than $∢B$ .

Calculate $∢A$ .

Step-by-step solution

To solve this problem, let's calculate $∢A$ with the steps outlined below:

Step 1: Write the equations for each angle based on the given conditions: $∢B = 2A$ $∢C = 3B = 3(2A) = 6A$
Step 2: Use the sum of angles in a triangle: $∢A + ∢B + ∢C = 180^\circ$ Substitute the expressions: $A + 2A + 6A = 180$
Step 3: Simplify the equation: $9A = 180$ Divide both sides by 9 to solve for $A$ : $A = \frac{180}{9} = 20$

Therefore, the solution to the problem is $∢A = 20^\circ$ .

Final Answer

20°

Key Points to Remember

Essential concepts to master this topic

Rule: Sum of triangle angles equals 180°, always use this fundamental property
Technique: Express all angles in terms of A: B = 2A, C = 6A
Check: Verify 20° + 40° + 120° = 180° equals triangle sum ✓

Common Mistakes

Avoid these frequent errors

Adding angle relationships incorrectly
Don't just add A + 2A + 3B = 180° without substituting! This creates an equation with two variables that can't be solved. Always substitute to express everything in terms of one angle first, then solve A + 2A + 6A = 180°.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

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FAQ

Everything you need to know about this question

Why do I need to express everything in terms of angle A?

You need one variable to solve the equation! Since B = 2A and C = 3B = 6A, expressing everything as multiples of A gives you one equation with one unknown.

How do I know that C = 6A and not just 3B?

Since B = 2A, you substitute: C = 3B = 3(2A) = 6A. This is substitution - replacing B with its equivalent expression in terms of A.

What if my angle calculations don't add up to 180°?

Check your substitutions! Make sure you correctly wrote $C = 3B = 3(2A) = 6A$ , then verify $A + 2A + 6A = 9A = 180°$ .

Can triangles have angle relationships like this in real life?

Absolutely! Many triangles have angles in specific ratios. For example, in a 1:2:6 ratio triangle like this problem, you get a very sharp triangle with angles 20°, 40°, and 120°.

Is there a faster way to solve this without algebra?

The algebraic method is actually the fastest way! You could guess and check, but setting up $A + 2A + 6A = 180°$ gives you the answer in just two steps.

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Triangle Angle Calculation: Finding Angle A When B=2A and C=3B

Triangle Angles with Algebraic Relationships

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to express everything in terms of angle A?

How do I know that C = 6A and not just 3B?

What if my angle calculations don't add up to 180°?

Can triangles have angle relationships like this in real life?

Is there a faster way to solve this without algebra?

🌟 Unlock Your Math Potential

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