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In the above theorem, after proving ∠B + ∠D = 180° , can you use another way to prove ∠A + ∠C = 180°?

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Yes, we can prove ∠A + ∠C = 180° by another way. 

∠B + ∠D = 180° 

In ABCD, 

∠A + ∠B + ∠C + ∠D = 360° [Sum of the measures of all angles of a quadrilateral is 360°.] 

∴ ∠A + ∠C + 180° = 360° 

∴ ∠A + ∠C = 360° – 180° 

∴ ∠A + ∠C = 180°

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