Question

find the value of x in the diagram

Answer 1

Short answer is 40
To solve x we need to consider a few things..
You can observe that there is a triangle where the two lines intersect.So,one angle of that triangle is 90°.Since,
90 + (angle of the triangle) = 180
angle of the triangle = 90.
the other angles can be found,since 130° = angle adjacent to the other angle of the triangle (corresponding angles).
So sum of the adjacent angles = 180
130 + (another angle of the triangle) = 180
another angle of the triangle = 50°
so the sum of the angles of the triangle = 180
50 + 90 + (last angle of the triangle) = 180
last angle of the triangle = 180 - 140 = 40°
The last angle of the triangle is vertically opposite to x,and therefore x = 40°.

Answer 2

See the attach file for ans