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Recent angle-resolved photoemission electron spectroscopy (ARPES) experiments demonstrate that the momentum dependence of the spectral gap in underdoped cuprates does not follow a pure $d$-wave form [H. Anzai et a., Nat. Comm. {\bf 4}, 1815 (2013)]. This deviation is highly controversial. It has often been interpretated as a proof of the non-superconducting origin of the antinodal gap in the underdoped regime. In this article, we show that the measured angular dependence of the spectral gap can be explained by the basic nature of pairs in high-T$_c$ cuprates. Hole pairs, or {\it pairons}, form as a result of the local antiferromagnetic environment on the scale $\xi_{AF}$, the magnetic coherence length. The spatial extension of the pairon wavefunction beyond first nearest neighbours gives rise to the anomalous angular dependence of the gap, in quantitative agreement with experiments. This simple interpretation strongly indicates a common origin of the nodal and antinodal gaps.

Single origin of the nodal and antinodal gaps in cuprates