Find the Alpha Angle in Triangle ABC with 89° Interior Angle

Q: Why does every triangle always add up to exactly 180°?

This is a fundamental property of triangles in flat (Euclidean) geometry. No matter what size or shape your triangle is, the three interior angles will always sum to 180°!

Q: How do I handle the mixed number 5½°?

Convert mixed numbers to decimals for easier calculation: $ 5\frac{1}{2} = 5.5 $. Then add normally: 89 + 5.5 = 94.5.

Q: What if I get a decimal answer instead of a mixed number?

Both forms are correct! $ 85.5° $ and $ 85\frac{1}{2}° $ represent the same angle. Choose the format that matches your answer choices.

Q: Can a triangle have angles that don't add to 180°?

Never in regular flat geometry! If your angles don't sum to 180°, double-check your arithmetic. This rule is always true for triangles.

Q: What if one of the given angles seems too big?

Check that each angle is less than 180°. In this problem, 89° and 5½° are both reasonable. If an angle equals or exceeds 180°, reread the problem carefully.

Triangle Angle Sum with Mixed Numbers

Find the measure 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 value of A

00:03 The sum of angles in a triangle equals 180

00:07 Substitute in the relevant values according to the given data and proceed to solve for A

00:12 Group terms

00:16 Isolate A

00:21 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the measure of the angle $\alpha$

Step-by-step solution

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$89+5\frac{1}{2}+\alpha=180$

$\alpha+94.5=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-94.5$

$\alpha=85.5$

Final Answer

$85\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Triangle Rule: Sum of all three interior angles equals 180°
Technique: Add known angles: 89° + 5½° = 94.5°
Check: Verify sum: 89° + 5½° + 85½° = 180° ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add all known angles before subtracting
Don't subtract each known angle separately from 180° = wrong calculation order! This creates confusion and arithmetic errors. Always add all known angles first, then subtract their sum from 180°.

Practice Quiz

Test your knowledge with interactive questions

Can a triangle have a right angle?

FAQ

Everything you need to know about this question

Why does every triangle always add up to exactly 180°?

This is a fundamental property of triangles in flat (Euclidean) geometry. No matter what size or shape your triangle is, the three interior angles will always sum to 180°!

How do I handle the mixed number 5½°?

Convert mixed numbers to decimals for easier calculation: $5\frac{1}{2} = 5.5$ . Then add normally: 89 + 5.5 = 94.5.

What if I get a decimal answer instead of a mixed number?

Both forms are correct! $85.5°$ and $85\frac{1}{2}°$ represent the same angle. Choose the format that matches your answer choices.

Can a triangle have angles that don't add to 180°?

Never in regular flat geometry! If your angles don't sum to 180°, double-check your arithmetic. This rule is always true for triangles.

What if one of the given angles seems too big?

Check that each angle is less than 180°. In this problem, 89° and 5½° are both reasonable. If an angle equals or exceeds 180°, reread the problem carefully.

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Find the Alpha Angle in Triangle ABC with 89° Interior Angle

Triangle Angle Sum with Mixed Numbers

❤️ 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 does every triangle always add up to exactly 180°?

How do I handle the mixed number 5½°?

What if I get a decimal answer instead of a mixed number?

Can a triangle have angles that don't add to 180°?

What if one of the given angles seems too big?

🌟 Unlock Your Math Potential

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