Question

Which of the following is true?
(i) A triangle can have two right angles.
(ii) A triangle can have all angles less than \[{60^ \circ }\].
(iii) A triangle can have two acute angles.
A. Only (ii)
B. Only (i)
C. Only (iii)
D. All are true

Answer 1

Hint: Here we should know about the angle sum property. It states that the sum of all the angles of a triangle is \[{180^ \circ }\]. We have to add all the angles and then we have to see whether its sum is coming up to \[{180^ \circ }\] or not.

Complete step by step answer:
In the above question, we have given three statements and we have to check them one by one to find the correct answer from the given options. To do this question we should remember that the sum of all the angles of a triangle is \[{180^ \circ }\].

In statement one, it is given that a triangle can have two right angles. If the triangle has two right angles, the sum of angles of the triangle will be more than \[{180^ \circ }\], which is not possible because the third angle cannot be zero degrees. Therefore, statement one is not correct.

In statement two, it is given that a triangle can have all angles less than \[{60^ \circ }\].If the triangle has all the angles less than \[{60^ \circ }\], the sum of the triangle will be less than \[{180^ \circ }\], which is not possible. Therefore, statement two is not correct.

In statement three, it is given that a triangle can have two acute angles. If the triangle has two acute angles, then the third angle can be a right angle or an obtuse angle and the sum of all can be equal to \[{180^ \circ }\].Therefore, it is possible.Therefore, statement three is correct.

Hence, option (C) is correct.

Note: The angle sum property of a triangle states that the sum of the angles of a triangle is equal to \[{180^ \circ }\]. A triangle has three sides and three angles, one at each vertex. Whether a triangle is an acute, obtuse, or a right triangle, the sum of its interior angles is always \[{180^ \circ }\].