Classify a Triangle: Angles A and B Both Less Than 90 Degrees

Q: If angles A and B are both less than 90°, what about angle C?

Since all triangle angles sum to $180^\circ$, and A + B $180^\circ$, angle C must also be less than $90^\circ$. This creates an acute triangle where all three angles are acute!

Q: Can a triangle have two angles less than 90° and still be a right triangle?

No! A right triangle has exactly one $90^\circ$ angle. If both A and B are less than $90^\circ$, then neither can be the right angle, so it cannot be a right triangle.

Q: Why is 'None of the options' sometimes the correct answer?

Sometimes the given diagrams don't match the stated conditions. If all triangles shown are right triangles but the problem requires acute angles only, then none of the visual options are correct!

Q: How do I identify if a triangle diagram shows a right angle?

Look for a square symbol at one cornerCheck if two sides appear perpendicular (meeting at exactly $90^\circ$)Right triangles often have one vertical and one horizontal side

Q: What's the difference between acute, right, and obtuse triangles?

Acute: All angles $90^\circ$Right: Exactly one angle = $90^\circ$Obtuse: One angle > $90^\circ$Remember: every triangle fits exactly one category!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's begin by choosing the correct triangle.

00:12 Pick the triangle where corners A and B are not forming a right angle.

00:18 Great! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Choose the appropriate triangle according to the given:

Angle B is less than 90 degrees

Angle A is less than 90 degrees

2

Step-by-step solution

To solve this problem, we need to identify what type of triangle aligns with having both given angles, Angle A and Angle B, less than $90^\circ$ .

Step 1: Understand that for any triangle, the sum of the internal angles is always $180^\circ$ .
Step 2: Since both Angle A and Angle B are less than $90^\circ$ , they are acute. A triangle with two acute angles implies that the third angle should also be acute because all angles should sum up to less than $180^\circ$ .
Step 3: We need to examine available options to determine if any comply with these properties of a triangle.

Now, let's analyze the given choices:

Choice 1 shows a triangle with a right angle, which contradicts the condition that both Angle A and Angle B are less than $90^\circ$ .
Choice 2 explicitly indicates that none of the options are correct, suggesting no triangle fits the conditions given in the problem statement.
Choice 3, similarly to Choice 1, can't have two angles being less than $90^\circ$ if one is a right angle.
Choice 4 again has a right angle, contradicting the initial condition.

All given diagrammatic options have a right angle (based on the SVG descriptions or their right-angled appearance), which directly violates the condition of both Angle A and Angle B being acute.

Therefore, the most appropriate answer is: None of the options.

3

Final Answer

None of the options.

Key Points to Remember

Essential concepts to master this topic

Rule: Triangle angles must sum to exactly $180^\circ$
Technique: Two acute angles (< $90^\circ$ ) require third angle also acute
Check: All three angles must be less than $90^\circ$ for acute triangle ✓

Common Mistakes

Avoid these frequent errors

Choosing right triangles when given acute angle conditions
Don't select triangles with $90^\circ$ angles when told angles A and B are both less than $90^\circ$ = contradicts given conditions! Right triangles have exactly one $90^\circ$ angle, violating the constraint. Always verify all angles match the stated conditions.

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

If angles A and B are both less than 90°, what about angle C?

+

Since all triangle angles sum to $180^\circ$ , and A + B < $180^\circ$ , angle C must also be less than $90^\circ$ . This creates an acute triangle where all three angles are acute!

Can a triangle have two angles less than 90° and still be a right triangle?

+

No! A right triangle has exactly one $90^\circ$ angle. If both A and B are less than $90^\circ$ , then neither can be the right angle, so it cannot be a right triangle.

Why is 'None of the options' sometimes the correct answer?

+

Sometimes the given diagrams don't match the stated conditions. If all triangles shown are right triangles but the problem requires acute angles only, then none of the visual options are correct!

How do I identify if a triangle diagram shows a right angle?

+

Look for a square symbol at one corner
Check if two sides appear perpendicular (meeting at exactly $90^\circ$ )
Right triangles often have one vertical and one horizontal side

What's the difference between acute, right, and obtuse triangles?

+

Acute: All angles < $90^\circ$
Right: Exactly one angle = $90^\circ$
Obtuse: One angle > $90^\circ$
Remember: every triangle fits exactly one category!

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Classify a Triangle: Angles A and B Both Less Than 90 Degrees

Triangle Classification with Angle Constraints

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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

If angles A and B are both less than 90°, what about angle C?

Can a triangle have two angles less than 90° and still be a right triangle?

Why is 'None of the options' sometimes the correct answer?

How do I identify if a triangle diagram shows a right angle?

What's the difference between acute, right, and obtuse triangles?

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