Question

如图,圆O中,弦AB、CD延长线交与P,AD、BC交于点M,若∠P=36°,∠AMC=80°,则∠MDC=_____

Answer 1

∵∠A=∠C,∠AMC=∠C+∠MDC=∠C+P+∠A

∴∠AMC=∠P+2∠A

∴80°=36+2∠A

∴∠A=22°

∴∠MDC=∠P+∠A=36+22=48°