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.

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

1

Understand the problem

Find the measure of the angle $\alpha$

2

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:

$\alpha=180-94.5$

$\alpha=85.5$

3

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

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

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

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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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