Final answer:
In triangle ΔTUV, with VT ≅ UV and m∆V = 98°, the measure of angle U (m∆U) is 41° since it is an isosceles triangle, and the sum of angles in any triangle is 180°.
Step-by-step explanation:
To find the measure of angle U (m∆U) in triangle ΔTUV, we know that VT ≅ UV which means triangle ΔTUV is an isosceles triangle with two equal sides and therefore two equal angles opposite those sides. As given, m∆V = 98° which is the vertex angle. In an isosceles triangle, the base angles are equal, so we need to find the value of the base angles (m∆T and m∆U).
The sum of angles in any triangle is 180°. Thus, m∆T + m∆U + m∆V = 180°. Substituting the given angle, we get m∆T + m∆U + 98° = 180°. Therefore, m∆T + m∆U = 180° - 98° = 82°.
Since m∆T = m∆U in an isosceles triangle, we can derive that 2 * m∆U = 82°. Dividing both sides by 2, we get m∆U = 41°.