Question

Find the value of x and give reasoning in the following image

Answer 1

x = 75°

Explanation:

Quadrilateral ABCD is a parallelogram.

`\implies seg\: AB|| seg\: DC`

(Opposite sides of a parallelogram)

`\implies m\angle A + m\angle B=180\degree`

(Interior angles on the same side of transversal)

`\implies 105\degree + m\angle B=180\degree`

`\implies m\angle B=180\degree-105\degree`

`\implies m\angle B=75\degree`

`seg \: AB || seg\: EF.....(Given)`

`\implies m\angle B =m\angle BEF`

(Alternate angles)

`\implies 75\degree =x`

`\implies \huge\red{\boxed{x =75\degree}}`