Question

In the given figure, l || m || n. If x: y = 5:4, then the
measure of angle z is
(a) 40°
(b) 50°
(c) 90°
(d) 80°​

Answer 1

Answer:

let x:y =5:4

5x,4x

x+y+z=180

5x+4x+z=180

9x+z=180

z=50°

Answer 2

Let x=5a and y=4a

Now ∠y+∠1=180  

 (Angle made on straight line (n) are supplementary)

⇒4a+∠1=180  

 

⇒∠1=180  

−4a..........(i)

Now m∣∣n and t is transversal

∴∠x=∠1   (Corresponding angles)

⇒5a=∠1

⇒5a=180  

∘

−4a

⇒9a=180  

 

⇒a=20  

Now ∠y=4a=4×20  

=80  

 

Now l∣∣n and t is transversal.

∴∠z=∠y  (Alternate angles)

⇒∠z=80