Question

If two angles of a triangle are acute angles, then third angle

• A. is less than the sum of the two angles
• B. is an acute angle
• C. is the largest angle of the triangle
• D. may be an obtuse angle

Answer 1

The correct option is D may be an obtuse angle

Case $I:$

If two angles are of ${60}^o$ then the third angle will also be ${60}^o$ which is an acute angle.

As ${60}^o+{60}^o+{60}^o={180}^o$

Case $II:$

If two angles are of ${30}^o$ then the third angle will be ${120}^o$ which is an obtuse angle.

As ${30}^o+{30}^o+{120}^o={180}^o$

$\therefore$ We can see, if two angles of a triangle are acute angles, then third angle will be acute angle or an obtuse angle.