# Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.

A =  80 °
B =  60 °
C =  120 °
D =  100 °

### Step-by-step explanation:

A = 4/5 D
B = 3x-15
C = 4x+20
A+D = 180
B+C = 180

A = 4/5·D
B = 3·x-15
C = 4·x+20
A+D = 180
B+C = 180

5A-4D = 0
B-3x = -15
C-4x = 20
A+D = 180
B+C = 180

Row 4 - 1/5 · Row 1 → Row 4
5A-4D = 0
B-3x = -15
C-4x = 20
1.8D = 180
B+C = 180

Row 5 - Row 2 → Row 5
5A-4D = 0
B-3x = -15
C-4x = 20
1.8D = 180
C+3x = 195

Row 5 - Row 3 → Row 5
5A-4D = 0
B-3x = -15
C-4x = 20
1.8D = 180
7x = 175

x = 175/7 = 25
D = 180/1.8 = 100
C = 20+4x = 20+4 · 25 = 120
B = -15+3x = -15+3 · 25 = 60
A = 0+4D/5 = 0+4 · 100/5 = 80

A = 80
B = 60
C = 120
D = 100
x = 25

Our linear equations calculator calculates it.

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Showing 1 comment:
Partho
Let Angle A=4x, B= 3x-15, C=4x+20 and D=5x.

Using the property that sum of adjacent angles = 180 we get:

A + D = 180 or 4x+5x=180.
Solving we get x=20.
Substituting we get: A=80, B=100

Similarly, B+C=180 or
3x-15+4x+20=180
Solving we get x=25
Substituting we get: B=60, D=120.

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