# Internal angles IST

Determine internal angles of isosceles trapezium ABCD /a, c are the bases/ and if:

alpha:gamma = 1:3

α =  45 °
β =  45 °
γ =  135 °
δ =  135 °

### Step-by-step explanation:

a=b
c=d
3a = 1c
a+b+c+d=360

a=b
c=d
3·a = 1·c
a+b+c+d=360

a-b = 0
c-d = 0
3a-c = 0
a+b+c+d = 360

Pivot: Row 1 ↔ Row 3
3a-c = 0
c-d = 0
a-b = 0
a+b+c+d = 360

Row 3 - 1/3 · Row 1 → Row 3
3a-c = 0
c-d = 0
-b+0.3333c = 0
a+b+c+d = 360

Row 4 - 1/3 · Row 1 → Row 4
3a-c = 0
c-d = 0
-b+0.3333c = 0
b+1.3333c+d = 360

Pivot: Row 2 ↔ Row 3
3a-c = 0
-b+0.3333c = 0
c-d = 0
b+1.3333c+d = 360

Row 4 + Row 2 → Row 4
3a-c = 0
-b+0.3333c = 0
c-d = 0
1.6667c+d = 360

Pivot: Row 3 ↔ Row 4
3a-c = 0
-b+0.3333c = 0
1.6667c+d = 360
c-d = 0

Row 4 - 1/1.66666667 · Row 3 → Row 4
3a-c = 0
-b+0.3333c = 0
1.6667c+d = 360
-1.6d = -216

d = -216/-1.6 = 135
c = 360-d/1.66666667 = 360-135/1.66666667 = 135
b = 0-0.33333333333333c/-1 = 0-0.33333333 · 135/-1 = 45
a = 0+c/3 = 0+135/3 = 45

a = 45
b = 45
c = 135
d = 135

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