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.

Correct result:

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

Solution:


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

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

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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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