Direct sum/Orthogonal spaces in dual space/Exercise

Let ${}V$ be a ${}K$-vector space, together with a direct sum decomposition

${}V=V_{1}\oplus V_{2}\,.$

Show that

${}{V}^{*}=V_{1}^{\perp }\oplus V_{2}^{\perp }\,$

holds, and that the restriction of the dual mapping

${V}^{*}\longrightarrow {V_{1}}^{*}$

onto ${}V_{2}^{\perp }$ is an isomorphism.

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