If `DeltaABC` is an obtuse angled triangle in which `angleC=110^(@)` then which one of the following is true ?

Options

A. `AB=AC`
B. `AB lt AC`
C. `AB gt AC`
D. `AB lt BC`

Answer

To solve the problem, we need to analyze the properties of triangle ABC, given that it is an obtuse-angled triangle with angle C measuring 110 degrees.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
We have triangle ABC, where angle C = 110 degrees. Since this is an obtuse triangle, one angle (angle C) is greater than 90 degrees.

2. **Sum of Angles in a Triangle**:
The sum of all angles in any triangle is always 180 degrees. Therefore, we can express the sum of angles A and B as:
\[ \text{Angle A} + \text{Angle B} = 180^\circ - \text{Angle C} \]
Substituting the value of angle C:
\[ \text{Angle A} + \text{Angle B} = 180^\circ - 110^\circ = 70^\circ \]

3. **Properties of Angles**:
Since angle A + angle B = 70 degrees, both angles A and B must be less than 70 degrees. This means both angles A and B are acute angles (less than 90 degrees).

4. **Identifying the Largest Angle**:
In triangle ABC, angle C is the largest angle (110 degrees). According to the properties of triangles, the side opposite the largest angle is the longest side. Therefore, the side opposite angle C (which is side AB) must be the longest side.

5. **Conclusion**:
Since angle C is the largest angle, the side opposite to it (AB) is the longest side. Thus, we can conclude:
\[ AB > AC \quad \text{and} \quad AB > BC \]

### Final Answer:
The correct statement is that side AB is the longest side in triangle ABC.