= Solution
Treat the two strands as newly formed <conjugate faults> obeying the same <Mohr-Coulomb failure criterion>, rather than merely inherited <faults> reactivated in a later <stress> field. A <fault strike> is an unoriented line, so $296^\circ$ is equivalent to $116^\circ$. The acute angle between the <fault strikes> is therefore $116^\circ-60^\circ=56^\circ$. The formal compressive acute bisector puts $\sigma_1$ at azimuth $88^\circ$ and $\sigma_3$ at $178^\circ$. This orientation must also be checked against the mapped senses of <strike-slip faulting>, as discussed below.
Let $\beta=28^\circ$ be the angle between either <fault plane> and $\sigma_1$. Tangency of <Mohr's circle> to $|\tau|=c+\mu\sigma'_n$, where $\sigma'_n$ is <effective stress> normal to the plane and $c$ is <cohesion>, gives $\beta=45^\circ-\phi/2$ and $\mu=\tan\phi$. Thus
$$
\phi=90^\circ-56^\circ=34^\circ,\qquad \boxed{\mu=\tan34^\circ\simeq0.675}.
$$
In the <Mohr circle>, the <fault planes> are $112^\circ$ apart around the circle, because a physical plane rotation is doubled. The figure uses $c=0$ to display both tangencies; a common nonzero <cohesion> changes the intercept, not the inferred <friction angle>. The inference of $\mu$ requires optimally oriented <conjugate faults> at formation: the two <fault strikes> alone cannot measure a friction coefficient for arbitrarily reactivated <faults>.
\b[Consistency limitation:] the mapped westward motion of the Anatolian block corresponds to <left-lateral strike-slip faulting> on the East Anatolian strand and <right-lateral strike-slip faulting> on the North Anatolian strand. East–west maximum compression for the acute-bisector construction instead predicts the opposite pair. The stress orientation compatible with the mapped senses lies near the north–south, obtuse bisector; the planes are then about $62^\circ$ from $\sigma_1$, which would give $\phi=90^\circ-2(62^\circ)=-34^\circ$ in the optimal-formation formula. A negative friction angle is inadmissible for ordinary frictional strength. Thus \b[$0.675$ is the formal magnitude inferred from unoriented angles, while the full map does not support a self-consistent positive-friction, optimally formed conjugate pair]. The common-stress assumption can still describe inherited or anisotropically controlled <faults>, but then their orientations no longer determine a unique coefficient.
\Image[/past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2023/paper-1-failure-mechanics.png]
{title=Conjugate-fault friction, reverse-fault stress directions, and shear versus tensile failure}
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