Question

In the figure given below a b angle d e and ac angle the AC prove that angle BAC is equal to angle E DF

Answer 1

Answer:

Step-by-step explanation:GivenABCDisaparallelogram.  

∠B&∠Careadjacentanglesintheparallelogram

so,∠B+∠C=180  

0

⇒∠B=180  

0

−∠C−−−(1)

GiventhatEB&ECareanglebisectorsfor∠B&∠Crespectively.

So,∠EBC=  

2

1

​

∠B&∠ECB=  

2

1

​

∠C

Nowin△BEC,∠EBC+∠ECB+∠CEB=180  

0

 

⇒  

2

1

​

∠B+  

2

1

​

∠C+∠CEB=180

⇒∠CEB+  

2

1

​

(∠B+∠C)=180

⇒∠CEB+  

2

1

​

×180=180  

0

{from(1)}

⇒∠CEB+90  

0

=180  

0

 

⇒∠CEB=90  

0

 

⇒∠CEB isa rightangle.