Question

In the adjoining figure, three coplanar lines AB,CD and EF intersect at point O, forming angles as shown.Find the values of x,y,z and t.

Say fast the answer.

Answer 1

X+50+90==180
x=40

x=y. vertically opposite angles
y=40
z=50. vertically opposite angles
t=90. vertically opposite angles

Answer 2

Answer:  The required values are

x= y = 40, z = 50  and  t = 90.

Step-by-step explanation:  Given that three co planar lines AB, CD and EF intersect at point O, forming angles as shown in the figure.

We are to find the values of x, y, z and t.

From the modified figure attached below , we can see that

∠BOC and ∠AOD are vertically opposite angles. So, we must have

$m\angle BOC=m\angle AOD=90^\circ\\\\\Rightarrow t^\circ=90^\circ\\\\\Rightarrow t=90.$

Now,

∠EOC and ∠FOD are also vertically opposite angles. So,

$m\angle EOC=m\angle FOD=50^\circ\\\\\Rightarrow z^\circ=50^\circ\\\\\Rightarrow z=50.$

Again, ∠EOF is a straight angle. So,

$m\angle EOF=180\circ\\\\\Rightarrow x^\circ+t^\circ+z^\circ=180^\circ\\\\\Rightarrow x+t+z=180\\\\\Rightarrow x+90+50=180\\\\\Rightarrow x=180-140\\\\\Rightarrow x=40.$

Now, since ∠EOA and ∠FOB are also vertically opposite angles. So,

$m\angle EOA=m\angle FOB\\\\\Rightarrow x^\circ=y^\circ\\\\\Rightarrow x=y=40.$

Thus, the required values are

x= y = 40, z = 50  and  t = 90.