= Solution
For an equilibrium <contact angle> measured through the <liquid>, <Young's equation> balances the tangential interfacial forces:
$$
\gamma_{SV}-\gamma_{SL}=\gamma_{LV}\cos\theta.
$$
The pure-<ethanol> measurement therefore fixes the solid–vapour <surface energy> as
$$
\gamma_{SV}=(21.0+21.4\cos23^\circ)\times10^{-3}
=40.699\times10^{-3}\,\mathrm{N\,m^{-1}}.
$$
\b[The inferred surface energy is $40.7\,\mathrm{mJ\,m^{-2}}$], equivalently $40.7\,\mathrm{mN\,m^{-1}}$. The equality of these units follows because creating interfacial <area> costs <energy>.
For the equal-fraction <mixture>, the stated linear relations give $\gamma_{SL}=20.5\,\mathrm{mN\,m^{-1}}$ and $\gamma_{LV}=28.5\,\mathrm{mN\,m^{-1}}$. Holding the solid–vapour <surface energy> fixed,
$$
\cos\theta_{1/2}=\frac{40.699-20.5}{28.5}=0.70873,
\qquad \boxed{\theta_{1/2}\simeq44.9^\circ.}
$$
The small decrease in $\gamma_{SL}$ increases the numerator of <Young's equation>, but the increase in $\gamma_{LV}$ has the larger relative effect and reduces $\cos\theta$. Consequently \b[the contact angle increases and the mixture wets the surface less well]. This inference uses equilibrium <wetting> on an unchanged smooth solid; a changing surface composition or <contact-angle hysteresis> would require additional measurements.
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