The problem states that we have an isosceles triangle $TVU$ with angle $UTV = 77^\circ$. We need to find the size of angle $TVU$.

1. Problem Description

The problem states that we have an isosceles triangle $TVU$ with angle $UTV = 77^\circ$. We need to find the size of angle $TVU$.

2. Solution Steps

Since triangle $TVU$ is an isosceles triangle and $TV = VU$, the angles opposite these sides are equal, i.e., $\angle VTU = \angle VUT$. Therefore, $\angle VUT = 77^\circ$.

The sum of the angles in a triangle is $180^\circ$. So,

$\angle TVU + \angle VTU + \angle VUT = 180^\circ$

$\angle TVU + 77^\circ + 77^\circ = 180^\circ$

$\angle TVU + 154^\circ = 180^\circ$

$\angle TVU = 180^\circ - 154^\circ$

$\angle TVU = 26^\circ$

3. Final Answer

The size of angle $TVU$ is $26^\circ$.