# Six-sided polygon

There is a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.

A =  63
B =  63
C =  126
D =  189
F =  90
e =  189

### Step-by-step explanation:

A=B
C = 2B
D = E
D = 3A
F = 90
A+B+C+D+E+F = (6-2) · 180

A=B
C = 2·B
D = e
D = 3·A
F = 90
A+B+C+D+e+F = (6-2) · 180

A-B = 0
2B-C = 0
D-e = 0
3A-D = 0
F = 90
A+B+C+D+F+e = 720

Pivot: Row 1 ↔ Row 4
3A-D = 0
2B-C = 0
D-e = 0
A-B = 0
F = 90
A+B+C+D+F+e = 720

Row 4 - 1/3 · Row 1 → Row 4
3A-D = 0
2B-C = 0
D-e = 0
-B+0.333333D = 0
F = 90
A+B+C+D+F+e = 720

Row 6 - 1/3 · Row 1 → Row 6
3A-D = 0
2B-C = 0
D-e = 0
-B+0.333333D = 0
F = 90
B+C+1.333333D+F+e = 720

Row 4 - -1/2 · Row 2 → Row 4
3A-D = 0
2B-C = 0
D-e = 0
-0.5C+0.333333D = 0
F = 90
B+C+1.333333D+F+e = 720

Row 6 - 1/2 · Row 2 → Row 6
3A-D = 0
2B-C = 0
D-e = 0
-0.5C+0.333333D = 0
F = 90
1.5C+1.333333D+F+e = 720

Pivot: Row 3 ↔ Row 6
3A-D = 0
2B-C = 0
1.5C+1.333333D+F+e = 720
-0.5C+0.333333D = 0
F = 90
D-e = 0

Row 4 - -0.5/1.5 · Row 3 → Row 4
3A-D = 0
2B-C = 0
1.5C+1.333333D+F+e = 720
0.777778D+0.333333F+0.333333e = 240
F = 90
D-e = 0

Pivot: Row 4 ↔ Row 6
3A-D = 0
2B-C = 0
1.5C+1.333333D+F+e = 720
D-e = 0
F = 90
0.777778D+0.333333F+0.333333e = 240

Row 6 - 0.77777777777778 · Row 4 → Row 6
3A-D = 0
2B-C = 0
1.5C+1.333333D+F+e = 720
D-e = 0
F = 90
0.333333F+1.111111e = 240

Row 6 - 0.33333333333333 · Row 5 → Row 6
3A-D = 0
2B-C = 0
1.5C+1.333333D+F+e = 720
D-e = 0
F = 90
1.111111e = 210

e = 210/1.11111111 = 189
F = 90/1 = 90
D = 0+e = 0+189 = 189
C = 720-1.3333333333333D-F-e/1.5 = 720-1.33333333 · 189-90-189/1.5 = 126
B = 0+C/2 = 0+126/2 = 63
A = 0+D/3 = 0+189/3 = 63

A = 63
B = 63
C = 126
D = 189
F = 90
e = 189

Our linear equations calculator calculates it. Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Do you have a system of equations and looking for calculator system of linear equations?