Question

Which of the following is a possible combination of the angles of a triangle?

• A. Obtuse, right and acute
• B. Obtuse, obtuse, acute
• C. Acute, acute, acute
• D. Right, right, right

Answer 1

The correct option is C Acute, acute, acute

As per the options given:

In option $A$,
obtuse angle + obtuse angle + acute angle.
Let the obtuse angle be
${91}^{\circ }$, and the acute angle be $x^{\circ }$ .
${91}^{\circ }+{91}^{\circ }+x^{\circ }>{180}^{\circ }$
Hence, a triangle with a sum greater than ${180}^{\circ }$ does not exist.

In option $B$,
obtuse angle + right angle + acute angle.
Let the obtuse angle be
${91}^{\circ }$, and the acute angle be $x^{\circ }$.
${91}^{\circ }+{90}^{\circ }+x^{\circ }>{180}^{\circ }$
Hence, a triangle with a sum greater than ${180}^{\circ }$ does not exist.

In option C,
acute angle + acute angle + acute angle.
Let the acute angles be ${60}^{\circ },{40}^{\circ },\text{and}{80}^{\circ }$.
${60}^{\circ }+{40}^{\circ }+{80}^{\circ }={180}^{\circ }$
Hence, a triangle with this combination is possible.

In option D,
right angle + right angle + right angle $>{180}^{\circ }$.
${90}^{\circ }+{90}^{\circ }+{90}^{\circ }={270}^{\circ }>{180}^{\circ }$
A triangle with a sum greater than ${180}^{\circ }$ does not exist.
So, only option C is a possible combination of the angles in a triangle.