Modern radar systems commonly utilize multiple-input multiple-output architectures, which often result in nonrectangular virtual antenna arrays. For these nonrectangular configurations, conventional angle estimation methods based on uniform linear array are suboptimal as they discard partial spatial information. Furthermore, subspace-based and iterative methods are often too computationally demanding for real-time applications. To address these limitations, this article proposes a computationally efficient two-stage angle estimation method, termed monopulse on nonrectangular array, designed to fully exploit the entire virtual aperture. The first stage introduces a unique amplitude-normalized 2-D discrete Fourier transform process to generate a robust coarse angle estimate from the nonrectangular array data. Building on this, the second stage employs a statistically optimized amplitude comparison monopulse technique to achieve off-grid high-precision fine estimation. Theoretical analysis, simulations, and experimental results demonstrate that the proposed method achieves high accuracy, approaching the Cram & eacute;r-Rao lower bound while maintaining a low computational cost.