1. **Stating the problem:** We have a quadrilateral ABCD with sides AB = 85 and AD = 35, and we want to find the angle at vertex A (\(\angle BAD\)). 2. **Understanding the triangle:** To find the angle at A, we consider triangle ABD where AB and AD are two sides meeting at A. 3. **Identifying sides relative to the angle at A:** - The side opposite to \(\angle BAD\) is BD (not given). - The side adjacent to \(\angle BAD\) can be either AB or AD depending on which angle we consider. - The hypotenuse is the longest side in a right triangle, but since we don't know if the triangle is right-angled, we use the Law of Cosines or trigonometric ratios if right angle is known. 4. **If the triangle is right-angled at D or B, we can use trigonometric ratios:** - Opposite side: side opposite to the angle. - Adjacent side: side next to the angle. - Hypotenuse: longest side opposite the right angle. 5. **Since only AB and AD are given, and the angle is unknown, we need more information (like side BD or if the triangle is right-angled) to find the angle at A.** 6. **Summary:** - Opposite side to \(\angle BAD\) is BD. - Adjacent sides are AB and AD. - Hypotenuse applies if the triangle is right-angled. Without additional data, we cannot calculate the exact angle but can identify the sides relative to the angle as above.