Question:
Is triangle ABC a right-angled triangle?
I) ABC has angles $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$.
II) The longest side is 10 units.
Is triangle ABC a right-angled triangle?
I) ABC has angles $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$.
II) The longest side is 10 units.
I) ABC has angles $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$.
II) The longest side is 10 units.
Show Hint
The definition of a right-angled triangle depends solely on its angles.
Updated On: Jun 26, 2026
- Statement I alone is sufficient
- Statement II alone is sufficient
- Statements I and II together are sufficient
- Statements I and II together are not sufficient
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Concept
A triangle is right-angled if one of its interior angles is $90^{\circ}$.
Step 2: Analysis of Statement I
The angles are given as $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$. Since one angle is $90^{\circ}$, it is definitively a right-angled triangle. Statement I alone is sufficient.
Step 3: Analysis of Statement II
Knowing the longest side is 10 units does not determine the angles of the triangle. Not sufficient.
Step 4: Conclusion
Statement I alone is sufficient, so the answer is (1). Final Answer: (1)
A triangle is right-angled if one of its interior angles is $90^{\circ}$.
Step 2: Analysis of Statement I
The angles are given as $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$. Since one angle is $90^{\circ}$, it is definitively a right-angled triangle. Statement I alone is sufficient.
Step 3: Analysis of Statement II
Knowing the longest side is 10 units does not determine the angles of the triangle. Not sufficient.
Step 4: Conclusion
Statement I alone is sufficient, so the answer is (1). Final Answer: (1)
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