Question

answer 12th question​

Answer 1

[ Note : refer the given figures in the attachment ]

Answer

$\boxed{\textbf{\large{angle x = 95 degree}}}$

To find

angle x = ?

Given

AB || DE

angle A = 125'

angle D = 140'

Construction

Draw a line OM between line AB And DE, which is parallel to the line AB and DE, so AB || OM || DE

Explanation

we have given ,

angle BAC = 125'

angle CDE = 140'

so, AB || OM

☑ therefor

angle BAC congruent to angle angle ACO

.........................(transverse angles)

☑ angle BAC = angle ACO = 125'

so, angle ACO+ angle ACM = 180'

....... ( linear pair)

125' + angle ACM = 180'

angle ACM = 180' - 125'

angle ACM = 180' - 125' = 55'

$\boxed{\textbf{\large{angle ACM = 55 degree}}}$

☑ we know,

if two lines are parallel , we draw a line intersecting both parallel lines then the interior angles form by the line joining the parallel lines are supplymentry

☑ In a constructed figure,

CM || DE and the line segment which interesting both parallel lines is line CD

☑ hence,

angle DCM + angle CDE =180'

angle DCM + 140' = 180'

angle DCM = 180' - 140'

= 40'

$\boxed{\textbf{\large{angle DCM = 40 degree }}}$

☑ therefor

angle x = angle ACM + angle DCM

= 55' + 40 '

= 95'

$\boxed{\textbf{\large{angle x = 95 degree }}}$