1. **Problem statement:** Find the measure of angle 2 ($m\angle 2$) in the rhombus WUTV where angles at vertices V and W are each 28°. 2. **Properties of a rhombus:** - All sides are equal in length. - Opposite angles are equal. - Diagonals bisect each other at right angles (90°). - Diagonals bisect the vertex angles. 3. Since $\angle V = 28^\circ$ and $\angle W = 28^\circ$, and opposite angles are equal, $\angle U = \angle T$. 4. The diagonals intersect at right angles, so the four angles formed at the intersection are all 90°. 5. The diagonals bisect the vertex angles, so each half of $\angle V$ and $\angle W$ is $\frac{28^\circ}{2} = 14^\circ$. 6. Angle 2 is adjacent to half of $\angle T$ and part of the right angle formed by the diagonals. 7. Since $\angle T$ is opposite $\angle V$, $\angle T = 28^\circ$. 8. The diagonal bisects $\angle T$, so half of $\angle T$ is $14^\circ$. 9. At the intersection, angle 2 plus half of $\angle T$ equals 90° because diagonals intersect at right angles: $$m\angle 2 + 14^\circ = 90^\circ$$ 10. Solve for $m\angle 2$: $$m\angle 2 = 90^\circ - 14^\circ = 76^\circ$$ **Final answer:** $$m\angle 2 = 76^\circ$$