Trapezoid 20873

In the trapezoid ABCD (AB II CD) is α = 57 °, γ = 4β. Calculate the size of all interior angles.

Correct answer:

A =  57
B =  36
C =  144
D =  123

Step-by-step explanation:


A = 57
C = 4·B
A+D = 180
B+C = 180

A = 57
4B-C = 0
A+D = 180
B+C = 180

Row 3 - Row 1 → Row 3
A = 57
4B-C = 0
D = 123
B+C = 180

Row 4 - 1/4 · Row 2 → Row 4
A = 57
4B-C = 0
D = 123
1.25C = 180

Pivot: Row 3 ↔ Row 4
A = 57
4B-C = 0
1.25C = 180
D = 123


D = 123/1 = 123
C = 180/1.25 = 144
B = 0+C/4 = 0+144/4 = 36
A = 57/1 = 57

A = 57
B = 36
C = 144
D = 123

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