Two prisms of identical geometrical shape are combined such that...

The net deviation produced by a combination of two prisms with oppositely directed refracting angles is the difference of their individual deviations.

For a thin prism, the deviation is given by $\delta = (\mu - 1)A$, where $\mu$ is the refractive index and $A$ is the angle of the prism.

Since the prisms have identical geometrical shapes, their refracting angles are equal. Let the angle of the prisms be $A$.

The net deviation $\delta_{net}$ is given by:

$\delta_{net} = \delta_2 - \delta_1$

$\delta_{net} = (\mu_2 - 1)A - (\mu_1 - 1)A$

$\delta_{net} = (\mu_2 - \mu_1)A$

Substituting the given values, \delta_{net} = 1.0^{}^{{}^{\circ}}, $\mu_1 = 1.52$, and $\mu_2 = 1.62$:

1.0^{}^{{}^{\circ}} = (1.62 - 1.52)A

1.0^{}^{{}^{\circ}} = 0.10 A

A = \dfrac{1.0^{}^{{}^{\circ}}}{0.10} = 10^{}^{{}^{\circ}}