Question

Give reasons for angle x being 75°​

Answer 1

Corresponding angles

Answer 2

Given -

• $\sf{\angle{EFG}=105\degree}$

To prove-

• x° = 75°

Solution-

Assumption

AD || EH

If AD || EH and CG is a transversal.

Then,

$\implies\sf{\angle{BFE+EFG}=180\degree\:(linear\:pair)}$

$\implies\sf{\angle{BFE+105\degree}=180\degree}$

$\implies\sf{\angle{BFE}=180\degree-\:105\degree}$

$\implies\bf{\angle{BFE}=75\degree}$

We know,

$\sf{\angle{BFE}=\angle{CBA}=75\degree\:(corresponding\:angles)}$

$\sf{\angle{BFE}=x\degree=75\degree}$

$\therefore\boxed{\bf{x\degree=75\degree}}$