Question

observe the given figure and fill in the blanks l is parallel to M and T be any transversal (a). Angle 1 and angle 2 are dash angles. (b). angle 7 and angle 8 are ____angles .(c). angle 4 and angle 3 are ____angles. (d).angle 7 and angle 6 are_____ angles. (e). angle 2 and angle 4 are _____ angles.​

Answer 1

Answer:

Step-by-step explanation:

In △ABC

AE=BE=EC (As △ABC is right angled)

So, ∠BCE=∠EBC (△BEC is isosceles)

∴∠EBC=∠C

In △BOD

∠OBD=90°−∠ODB (Right angled triangle)

∠ODB=90°−∠C

tan(∠ODB)=  

BD

AB

​  

=  

a/2

C

​  

 

tan(90−C)=  

a/2

C

​  

 

∴cotC=  

a

2C

​  

→1

But in △ABC

tanC=  

a

C

​  

→2

Substituting 2 in 1

cotC=2tanC

∴tan  

2

C=  

2

1

​  

 

∴tanC=  

2

​  

 

1

​  

 

∴C=tan  

−1

(  

2

​  

 

1

​  

)