3條f.2升f.3數學(三角形的角)(10點!!)

1.
(a)
外角為 x 的內角 = 180° - x

(180° - x) + 121° + 52° + 112° = 360° (四邊形內角和)
465° - x = 360°
x = 105°

(b)
ÐC 的外角 = 180° - x

(180° - x) + 42° + 65° + 76° + 80° = 360° (多邊形外角和)
443° - x = 360
x = 83°


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2.
正六邊形內角
= (2*6 - 4)*90°/6
= 120°

x = 120°

ΔABC 為等邊三角形，AB = BC
所以 ÐBAC = ÐBCA = y (等腰Δ底角)
ÐBAC + ÐABC + ÐBCA = 180° (Δ內角和)
y + 120° + y = 180°
2y = 60°
y = 30°

ΔBCK中:
ÐKCB = y = 30°
ÐKBC = 120° - ÐKBF = 120° - 30° = 90°
z = ÐKCB + ÐKBC
z = 30° + 90°
z = 120°

1.a) X=180-(((4-2)*180)-121-112-52)
=180-(360-121-112-52)
=180-75
=105

1.b) X=180-(360-(80+75+65+42))
=180-(360-98)
=82

2.) X=(6-2)*180/6
=4*30
=120

Y=(180-X)/2
=(180-120)/2
=30

Z=180-(180-(X-Y)-Y)
=180-(180-(120-30)-30)
=180-60
=60