∠MSN =180° -(∠SMN+∠SNM) =180° -(30° +25°) =180°-55° =125°.
∠MSK = ∠SMK = 30° (ΔMSK_равнобедренный ,KM =KS) ;
∠MKS =180° -2*30° =120° ; ∠SKP =180°- ∠MKS=180°-120° =60°
|| или ∠SKP=60° как внешний угол треугольника MKS || .
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∠PSN = ∠PNS = 25° (ΔMSK_равнобедренный , PN =PS) .
∠NPS = 180° -2*25° =180°-50° =130°; ∠SPK =180°-∠NPS=180°-130°=50°.
∠KSP =180° - (∠SKP+∠SPK) = 180° - (60°+50°) =70°
||или ∠KSP =∠MSN -(∠MSK+∠PSN ) =125°-(30°+25°) =125° -55°=70° ||.
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∠ADC =360° - (360°- (20° +130°+15°)) = 165°.
cумма углов четырехугольника (в данном случае ABCD) равна 360°.
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∠ADC =360°-(∠ADB +∠CDB) =
360°- ( (180° -(∠DAB +∠DBA) +(180° -(∠DCB +∠DBC) ) =
360°- (360°-(20° +15° +∠DBA +∠DBC ) )=
360°- ( 360°- (20° +15° +130°) ) = 165°.