CTET Paper II (Mathematics and Science) 23 Dec 2021 Solved Paper

Concept:The sum of the three interior angles of a triangle is always $180^\circ$.The triangle inequality states that the sum of any two sides is greater than the third side.Explanation:Check each statement one by one.Option A: A triangle can have all acute angles if each is less than $90^\circ$ and their sum is $180^\circ$. Example: $60^\circ, 60^\circ, 60^\circ$. This is true.Option B: This is the triangle inequality theorem. It is always true.Option C: A triangle cannot have two obtuse angles because their sum would exceed $180^\circ$. So only one obtuse angle is possible. True.Option D: This is false. In an obtuse triangle, the obtuse angle can be greater than the sum of the other two acute angles. For instance, angles $30^\circ, 30^\circ, 120^\circ$: sum of two angles $30^\circ+30^\circ=60^\circ$ is not greater than $120^\circ$. Hence, statement D is not correct.Answer:Option D: Sum of any two angles of a triangle is greater than the third angle.