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The eighth grade mathematics textbook of Beijing Normal University.
Solution: from the meaning of the question: ∠ 1=∠2, ∠3=∠4.

∠∠2+∠M+∠7 = 180,∠ 1+∠5+∠B= 180

∴∠M+∠7=∠5+∠B

∠∠3+∠6+∠M = 180,∠4+∠D+∠8= 180

∴∠6+∠M=∠8+∠D

∠5=∠6, ∠7=∠8.

∴2∠M=∠B+∠D

That is ∠M= 1/2(∠B+∠D).

The corner has been marked in the picture.

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