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

Question

asked Jul 18, 2023 151k views

1 Answer

Artem Tutov · Answer 1 · 2023-07-23T06:08:00+0000

Answer:

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)

$\implies 75\degree =x$

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