In a Δ ABC, (c + a + b)(a + b - c) = ab. The measure of the angle C is:
\[ (a + b)^2 - c^2 = ab \] \[ a^2 + b^2 + 2ab - c^2 = ab \] \[ a^2 + b^2 + ab - c^2 = 0 \] \[ a^2 + b^2 - c^2 = -ab \] We know, \[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \] Substituting, \[ \cos C = \frac{-ab}{2ab} = -\frac{1}{2} \] \[ \Rightarrow C = \frac{2\pi}{3} \]
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