Question

in the given figure, ab||xy, angle abz=65 degree, angle bzy=20 degree. calculate angle xyz

Answer 1

Given:

Given that, ab||xy and $\angle{abz} = 65^0$ and $\angle bzy = 20^0$.

To find:

We have to find the value of $\angle xyz$.

Solution:

To find $\angle xyz$ let us try to visualize the diagram.

There are two parallel lines up and down and at the middle of this two line there is a point z and lines from this point touches with b and y respectively.

Now,

Let us draw an imaginary line mn passing through point z and parallel to ab and xy.

Interior $\angle bzy = 20^0$

Exterior $\angle bzy$ = (360 - 20) = $340^0$

Now $\angle abz + \angle bzm = 180^0$ [co-interior angle]

∴$\angle bzm =$ (180 - 65 ) = $115^0$

And,

$\Rightarrow \angle bzy$ = $\angle bzm$ + $\angle mzy$

$\Rightarrow 340^0$ = $115^0$ +  $\angle mzy$

$\Rightarrow \angle mzy$ $= (340 - 115 ) =$ $225^0$

Now again $\angle mzy$ + $\angle xyz$ = $180^0$

$\angle xyz$  = (180 - 225 ) = $-45^0$

As, the angle is in negative. It is a Hypothetical question.

So, we cannot calculate the angle.