Question

In the given figure AB is parallel to CD, find the value of z.
(a) 70°
(b) 80-
(c) 90
(d) 135
35​

Answer 1

Answer:

Construction- Draw a straight line parallel to lines AB and CD and passing through point E. Name it FG.(Extend it a bit more than angle z.)

Now,

Angle FEB+Angle ABE=180⁰(co- interior angles)

or, Angle FEB+35⁰=180⁰

or, Angle FEB=180⁰-35⁰=145⁰

Again,

Angle CDE+ Angle FED=180⁰(co- interior angles)

or, 45⁰+Angle FED=180⁰

or, Angle FED=180⁰-45⁰=135⁰

Now, notice that

One part of angle z forms linear pair with angle FEB and the other part forms linear pair with angle FED.

Let z=angle x+angle y.

Therefore,

145⁰+x=180⁰

or, x=35⁰

And,

135⁰+y=180⁰

or, y=45⁰

Therefore, angle z=(x+y)=(35+45)⁰=80⁰.

Therefore, option B is correct.