Question

In Fig. find the values of rand v and then
show that AB || CD.
50°​

Answer 1

$\huge \fbox{Correct Question:}$

$\sf{In \: fig. 6.28,find \: the \: values \: of \: x \: and \: y \: and \: then \: show} \\ \sf{that \: AB||CD. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\huge \fbox{Answer:}$

$\large \underline{ \underline{\frak{ \color{red}Given:}}}$

$\mapsto \sf{ \angle A \cal x \cal l=50°}$

$\mapsto \sf{ \angle C \cal y \cal l=130°}$

$\large \underline{ \underline{\frak{ \color{green}To \: find:}}}$

$\leadsto \sf{ \angle \cal x}$

$\leadsto \sf{ \angle \cal y}$

$\large \underline{ \underline{\frak{ \color{blue}Property \: used:}}}$

${\rightarrow \sf{Vertically \: opposite \: angle \: are \: equal.}}$

${ \rightarrow \sf{Alternate \: interior \: angles \: are \: equal. }}$

$\large \underline{ \underline{\frak{ \color{indigo}According \: to \: Question:}}}$

$: : \implies \sf{ \angle C {\cal yl} = \angle D {\cal yl}}$

$: : \implies \sf{ \angle D {\cal yl} = 130°}$

$: : \implies \sf{ \angle D {\cal yl} = \angle A {\cal xl}}$

$: : \implies \sf{ \angle A {\cal xl} = 130°}$

${: : \implies \sf{AB||CD \:because \: alternate \: interior\: angle \: is \: equal.}}$

Answer 2

Step-by-step explanation:

Given:

The measurement of the angles are 50° and 130°

To find:

The value of the x and y

To prove:

AB ∥ CD

Solution:

From the figure:

x+50° = 180° [Linear pair]

x = 180°-50°

x = 130°

and

y = 130° [ vertically opposite angle]

The value of x and y is 130° and 130° respectively

As we have found the value of x and y and we can see that the value of x and y are equal to each other

and from the figure, we can see that the and x and y is the alternate interior angle for the lines AB and CD

So the lines AB and CD must be Parallel to each other

Hence Proved