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The slanting line, the side of the big triangle and the base form a small triangle on the right. Its angle at the base vertex is $$180^\circ - c$$, its angle where the line cuts the side is $$e$$, and its angle on the base line is $$180^\circ - g$$. Adding these gives $$(180^\circ - c) + e + (180^\circ - g) = 180^\circ$$, so $$c = e + (180^\circ - g)$$.
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