Question

In trapezium ABCD, AB // DC, angle B = 60 degrees and AD = BC, if AD = BC= 10 cm., DC = 20 cm.,find AB. *
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Answer 1

Answer:

Step-by-step explanation:

Through B, draw a straight line parallel to AD which meets CD at E.

Now, since AB∥DE and AD∥BE,

∴ABED is a parallelogram.

Thus, ED=AB=18cm

As, BE∥AD and CD is a transversal,

∴∠BED=∠D=60  

o

(∵∠ABE=∠D).

Since, in an isosceles trapezium, the base angles are equal, ∠C=∠D=60  

o

.

In ΔBEC,∠BEC+∠ECD+∠CBE=180  

o

 

(Angle sum property of a triangle)

⇒60  

o

+60  

o

+∠CBE=180  

o

 

⇒120  

o

+∠CBE=180  

o

 

⇒∠CBE=180  

o

−120  

o

 

⇒∠CBE=60  

o

 

As the measure of ∠BEC=60  

o

,∠ECB=60  

o

 and ∠CBE=60  

o

,ΔCBE is an equilateral triangle, Thus

∴CE=BC=12cm(BC=AD=12cm)

Now, CE+ED=12+18

⇒DC=30cm