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1. ABC C 45, AD , CAD 30. B.
:
ABC. AD , BAD CAD :
BAD = CAD = 30. , BAC = BAD + CAD = 30 + 30 = 60. 180. :
A + B + C = 180;
60 + B + 45 = 180;
B = 75.
: 75º
2. ABC AC = BC, C 40. DBC.
:
, ABC : AC = BC. , : A = ABC = x. 180, :
A + ABC + C = 180;
x + x + 40 = 180;
2 x = 140;
x = 70.
, ABC 70. ABC DBC , 180. :
ABC + DBC = 180;
70 + DBC = 180;
DBC = 110.
: 110
3. ABD A 48, C 56. BD = BC. D.
:
BCD BD = BC, D BCD ,
D = BCD = x.
|
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ACD = ACB + DCB = 56 + x.
ADC. 180, :
Ð A + Ð D +Ð ACD = 180;
48 + x + 56 + x = 180;
2 x + 104 = 180;
2 x = 76;
x = 38.
: 38
4. , A C ABC, 3 , 2 AC 1 B. ABC.
:
ED . AB = 2 ED.
ED = , = 2 . : ED = 3, ED = A 2, ED = B 1.
: = 2 3, = 3, ED = 3. = 5, = 4. , . .
: 12
5. 80. .
:
, .
: + = 128 + = 128
1) = = + = 128, 2 = 128, = 64, = 180 128 = 52
2) = = + = 128, + + = 180, , = 180 252= 76
: 64, 64, 52 52, 52, 76