We are asked to find the measures of angles 1, 2, 3, 4, and 5 in the given rectangle. We are given that one angle is $61^\circ$. Since it is a rectangle, we know that all the angles are $90^\circ$.

1. Problem Description

We are asked to find the measures of angles 1, 2, 3, 4, and 5 in the given rectangle. We are given that one angle is $61^\circ$. Since it is a rectangle, we know that all the angles are $90^\circ$.

2. Solution Steps

First, since the given shape is a rectangle, all of its corners are $90^\circ$ angles. Therefore,

$\angle 5 = 90^\circ$

$\angle 3 = 90^\circ$

The angle formed by the diagonal at vertex 4 is given as $61^\circ$. Therefore, $\angle 4 = 61^\circ$.

Since $\angle 4 + \angle 5 = 90^\circ$, and the triangle is inscribed in a rectangle, the angle adjacent to $\angle 4$ inside the right triangle must be $61^\circ$.

Then since it is a rectangle $\angle 5 = 90^\circ$ and $\angle 3 = 90^\circ$ and $\angle 4 = 61^\circ$ we can find $\angle 1$ and $\angle 2$:

$\angle 1 + \angle 4 = 90^\circ$

$\angle 1 + 61^\circ = 90^\circ$

$\angle 1 = 90^\circ - 61^\circ = 29^\circ$

Because the two triangles formed by the diagonal are congruent:

$\angle 2 = \angle 4 = 61^\circ$.

We already have $\angle 3 = 90^\circ$ and we are given $\angle 4 = 61^\circ$.

$\angle 5 = 90^\circ$

Thus, $\angle 1 = 29^\circ$, $\angle 2 = 61^\circ$, $\angle 3 = 90^\circ$, $\angle 4 = 61^\circ$, $\angle 5 = 90^\circ$.

3. Final Answer

$\angle 1 = 29^\circ$

$\angle 2 = 61^\circ$

$\angle 3 = 90^\circ$

$\angle 4 = 61^\circ$

$\angle 5 = 90^\circ$