Question

in the given figure AB||CD||FE,find the angles x and y​

Answer 1

Answer:

X = 105 degree

Y = 50 degree

Step-by-step explanation:

AB parallel FE parallel CD.

BC is transversal.

Extend FE so as to intersect it to BC at point G.

Now, B-G-C and G-F-E.

Angle ABC = Angle BGE or BGF=75 degree.

... Alternate angles.

Angle BGE + Angle CGE =180 degree.

...Interior angles.

Hence, Angle CGE = Angle X = 180-75=105 degree.

Also,

Angle GCD = Angle BGE

...Corresponding angles.

Hence, Angle GCD. = 75 degree.

But, Angle GCD = Angle Y + Angle FCD. (Angle Addition Property)

Hence,

Angle Y= 75-25=50 degree.